Abstract
The survey is devoted to the theory of retracts and infinite-dimensional manifolds. The basic constructions and concepts are considered, and major attention is given to properties of mappings of softness type.
Similar content being viewed by others
Literature cited
S. A. Antonyan, “Retracts in categories of G-spaces,” Izv. Akad. Nauk ArmSSR,15, No. 5, 365–378 (1980).
S. A. Antonyan, “Retracts in the category of G-spaces,” Bull. Acad. Pol. Sci. Ser. Sci. Math.,28, No. 11–12, 613–618 (1980).
V. M. Babich, “On the question of extending functions,” Usp. Mat. Nauk,8, No. 2, 111–113 (1953).
V. N. Basmanov, “Onl 2-stability of spaces of homeomorphisms of metric spaces,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 37–40 (1982).
V. N. Basmanov, “On functions taking connected ANR-bicompacta into simply connected spaces,” Preprint, Moscow State University (1983).
S. A. Bogatyi, “On n-mobility in the sense of K. Borsuk,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,22, No. 8, 821–825 (1974).
S. A. Bogatyi and Gencho S. Skordev, “A theorem on fixed points for NE-mappings,” Serdika. Bulg. Mat. Spisanie,3, No. 2, 126–129 (1977).
K. Borsuk, “On the concept of a divisor and a multiple mapping,” Byul. Pol'sk. AN,3, No. 2, 81–85 (1955).
K. Borsuk, “On the concept of dependence of continuous mappings,” Byul. Pol'sk. AN,3, No. 5, 248–250 (1955).
G. L. Garg, “An analog of the Kuratowski-Dugundji theorem for the category of metrizable uniform spaces with uniformly continuous mappings,” Dokl. Akad. Nauk SSSR,195, No. 2, 266–269 (1970).
G. L. Garg, “A necessary and sufficient condition in order that a metric space can be uniformly retracted onto each nonempty, closed subset of it,” Sib. Mat. Zh.,12, No. 1, 222–225 (1971).
G. L. Garg, “An analog of the Kuratowski-Dugundji theorem,” Fundam. Math.,83, No. 1, 85–96 (1973).
V. Gol'shtynskii, “On extension of mappings into the sphere from one term to a countable sum,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,16, No. 5, 383–387 (1968).
D. Doichinov, “On the uniform shape of metric spaces,” Dokl. Akad. Nauk SSSR,226, No. 2, 257–260 (1976).
A. N. Dranishnikov, “On countable-valued retracts of the Tikhonov cube,” Usp. Mat. Nauk,36, No. 3, 211–212 (1981).
Zharko Zhivanovich, “Neighborhood contractions and absolute neighborhood contractions in metric spaces,” Math. Balkan., No. 4, 731–743 (1974).
Zharko Zhivanovich, “Quasi-extendable mappings,” Mat. Vesn.,2, No. 1, 59–67 (1978).
M. M. Zarichnyi, “The functor λn and absolute retracts,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 4, 15–19 (1982).
M. M. Zarichnyi, “Preservation of ANR of (\(\mathfrak{M}\))-spaces and infinite-dimensional manifolds by some covariant functors,” Dokl. Akad. Nauk SSSR,271, No. 3, 524–528 (1983).
M. M. Zarichnyi, “On hypersymmetric powers of supercompacta,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 18–21 (1983).
A. V. Ivanov, “On superextensions λnX,” Usp. Mat. Nauk,36, No. 3, 213–1214 (1981).
A. V. Ivanov, “Superextensions of openly generated bicompacta,” Dokl. Akad. Nauk SSSR,259, No. 2, 275–278 (1981).
A. V. Ivanov, “Solution of a problem of van Mill on characterization of bicompacta,” Dokl. Akad. Nauk SSSR,262, No. 3, 526–528 (1982).
A. V. Ivanov, “A superextension of the Tikhonov cube Iτ homeomorphic to Iτ,” Mat. Zametki,33, No. 5, 763–772 (1983).
S. D. Iliadis, “The concept of a retract in categories,” Math. Balkan.,8, No. 14, 121–130 (1978).
V. A. Kalinin, “Approximation retracts for a class of bicompact spaces,” Sib. Mat. Zh.,16, No. 4, 722–735 (1975).
V. A. Kalinin, “Representation of absolute shape retracts in the form of an intersection of Tikhonov cubes,” Dokl. Akad. Nauk SSSR,227, No. 5, 1045–1048 (1976).
A. Kosinskii, “A topological characterization of two-dimensional polyhedra,” Byul. Pol'sk. AN,2, No. 7, 325–327 (1954).
K. Kuratowski, “A theorem on complete spaces and its applications to the investigation of local connectedness,” Byul. Pol'sk. AN,3, No. 2, 75–80 (1955).
A. B. Kurovskii and Yu. M. Smirnov, “On the dimension of Ird defined by means of retractions,” Czech. Mat. J.,26, No. 1, 30–36 (1976).
R. S. Linichuk, “On the spectral representation of λ-hyperspaces,” Dokl. Akad. Nauk UkrSSR, A, No. 10, 883–885 (1978).
Yu. T. Lisitsa, “Extension of mappings and a factorization theorem,” Dokl. Akad. Nauk SSSR,207, No. 5, 1042–1043 (1972).
Yu. T. Lisitsa, “On spaces connected and locally connected in all dimensions,” Fundam. Math.,80, No. 1, 35–45 (1973).
A. G. Lutsenko, “On retracts of Dτ,” Mat. Zametki,31, No. 3, 433–442 (1982).
S. Mardeshich and A. P. Shostak, “On the homotopy type of ANR for feathery final-compact spaces,” in: Topological Spaces and Their Mappings, Riga (1981), pp. 124–129, 184.
G. M. Nepomnyashchii, “On the equivalence of some properties of continuous mappings,” Czech. Mat. J.,29, No. 3, 378–384 (1979).
G. M. Nepomnyashchii, “On the spectral decomposition of multivalued absolute retracts,” Usp. Mat. Nauk,36, No. 3, 221–222 (1981).
G. M. Nepomnyashchii and Yu. M. Smirnov, “On retraction of mappings,” Czech. Mat. J.,29, No. 3, 366–377 (1979).
S. M. Nikol'skii, “On extension of functions of several variables with preservation of differential properties,” Mat. Sb.,40, No. 2, 243–268 (1956).
B. A. Pasynkov, “On the extension of continuous mappings,” Dokl. Akad. Nauk SSSR,219, No. 1, 39–42 (1974).
M. M. Postnikov, “Investigations in the homotopy theory of continuous mappings,” Tr. Mat. Inst. Akad. Nauk SSSR,46 (1955).
M. M. Postnikov, “Investigations in the homotopy theory of continuous mappings. III. General extension and classification theorems,” Mat. Sb.,40, No. 4, 415–452 (1968).
Yu. M. Smirnov, “Thickenings on bicompacta and the connection with bicompact extensions and with retraction,” Fundam. Math.,63, No. 2, 199–211 (1968).
M. V. Smurov, “On topological inhomogeneity of spaces of Kτ type,” Dokl. Akad. Nauk SSSR,255, No. 3, 526–531 (1980).
A. D. Taimanov, “On extension of continuous mappings of topological spaces,” Mat. Sb.,31(73), No. 2, 459–463 (1952).
A. D. Taimanov, “On the extension of continuous mappings into open sets,” Proc. 3rd All-Union Math. Congress, Moscow, Izv. Akad. Nauk SSSR, 135–136 (1956).
U. Tashmetov, “On connectedness and local connectedness of some hyperspaces,” Sib. Mat. Zh.,15, No. 5, 1115–1130 (1974).
V. V. Fedorchuk, “Probability measures and absolute retracts,” Dokl. Akad. Nauk SSSR,255, No. 6, 1329–1333 (1980).
V. V. Fedorchuk, “Covariant functors in the category of compacta, absolute retracts, and Q-manifolds,” Usp. Mat. Nauk,36, No. 3, 177–195 (1981).
V. V. Fedorchuk, “On open mappings,” Usp. Mat. Nauk,37, No. 4, 187–188 (1982).
V. V. Fedorchuk, “Exponentials of Peano continua — fiber version,” Dokl. Akad. Nauk SSSR,262, No. 1, 41–44 (1982).
N. G. Khadzhiivanov, “On extension of mappings into the sphere,” Godishn. Sofiisk. Univ. Mat. Fakt., 1969–1970,64, 1–6 (1971).
N. G. Khadzhiivanov, “Extension of mappings into spheres and the problem of P. S. Aleksandrov on bicompact thickenings,” Dokl. Akad. Nauk SSSR,194, No. 3, 525–527 (1970).
N. G. Khadzhiivanov, “On extension of mappings into spheres and on countable decompositions of Tikhonov cubes,” Mat. Sb.,84, No. 1, 119–140 (1971).
Ya. N. Khaimov, “On an increasing sequence of retracts,” Izv. Akad. Nauk TadzhSSR, Otd. Fiz.-Mat. Geol. Khim. Nauk, No. 3, 6–12 (1978).
P. V. Chernikov, “On extension of mappings with values in a metric space. II,” Preprint, Redkol. Sib. Mat. Zh., Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1979).
P. V. Chernikov, “On extension of mappings with values in a metric space. III,” Preprint, Redkol. Sib. Mat. Zh., SOAkad. Nauk SSSR, Novosibirsk (1980).
P. V. Chernikov, “On extension of mappings with values in a metric space. IV,” Preprint, Redkol. Sib. Mat. Zh., SO Akad. Nauk SSSR, Novosibirsk (1980).
E. V. Shchepin, “The topology of limit spaces of uncountable inverse spectra,” Usp. Mat. Nauk,31, No. 5, 191–226 (1976).
E. V. Shchepin, “A finite-dimensional, bicompact, absolute neighborhood retract is metrizable,” Dokl. Akad. Nauk SSSR,233, No. 3, 304–307 (1977).
E. V. Shchepin, “Infinite-dimensional topology,” Usp. Mat. Nauk,32, No. 5, 164 (1977).
E. V. Shchepin, “On Tikhonov manifolds,” Dokl. Akad. Nauk SSSR,246, No. 3, 551–554 (1979).
J. M. Aarts and T. Nishiura, “The Eilenberg-Borsuk duality theorem,” Proc. Kon. Ned. Akad. Wetensch.,A75, No. 1, 68–72 (1972).
Silvana Abeasis and Alberto Del Fra, “Osservazioni sul tipo omotopico dei G-CW-complessi e dei G-ANR,” Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis., Mat. Natur.,61, No. 1–2, 62–66 (1976) (1977).
A. A. Alemzadeh, “Retractions in differential topology,” Quart. Bull. Fac. Sci.,7, No. 1, 25–35 (1975).
R. D. Anderson, “Some remarks on totally disconnected sections of monotone open mappings,” Bull. Acad. Pol. Sci., cl. 3, 4, No. 6, 329–330 (1956).
R. D. Anderson, “One dimensional continuous curves,” Proc. Nat. Acad. Sci. USA,42, No. 10, 760–762 (19560.
R. D. Anderson, “Problems of group actions of Q-manifolds,” London Math. Soc. Lect. Note Ser., No. 26, 249–258 (1977).
R. D. Anderson. T. A. Chapman, and R. M. Schori, “Problems in the topology of infinitedimensional spaces and manifolds,” Rept. Math. Cent., ZW, No. 1, 24 (1971).
R. D. Anderson, D. W. Henderson, and J. F. West, “Negligible subsets of infinite-dimensional manifolds,” Compos. Math.,21, No. 2, 143–150 (1969).
R. D. Anderson and N. Kroonenberg, “Openproblems in infinite-dimensional topology,” Math. Centre Tracts, No. 52, 141–175 (1974).
R. D. Anderson and J. D. McCharen, “On extending homeomorphisms to Fréchet manifolds,” Proc. Am. Math. Soc.,25, No. 2, 283–289 (1970).
R. D. Anderson and R. M. Schori, “Factors of infinite-dimensional manifolds,” Trans. Am. Math. Soc.,142, 315–330 (1969).
Kiyoshi Aoki, “Note on deformation retract,” Proc. Jpn. Acad.,30, No. 7, 538–541 (1954).
G. Aquaro, “Funzioni reali uniformemente separate negli spazii uniformi ed applicazioni agli spazii normali,” Ann. Mat. Pura. Ed. Appl.,39, 401–409 (1955).
R. Arens, “Extension of coverings, of pseudometrics, and of linear-space-valued mappings,” Can. J. Math.,5, No. 2, 211–215 (1953).
S. Armentrout, “On the singularity of Mazurkiewicz in absolute neighborhood retracts,” Fund. Math.,69, No. 2, 131–145 (1970).
S. Armentrout, “A Bing-Borsuk retract which contains a two-dimensional absolute retract,” Rozpr. Mat., No. 123, 44 (1975).
S. Armentrout, “Decompositions and absolute neighborhood retracts,” Lect. Notes Math.,438, 1–5 (1975).
B. J. Ball and J. Ford, “Spaces of ANRs,” Fundam. Math.,77, No. 1, 33–49 (1972).
B. J. Ball and J. Ford, “Spaces of ANRs. II,” Fundam. Math.,78, No. 3, 209–216 (1973).
A. F. Bartholomay, “Type-invariance and h-retraction,” Port. Math.,13, No. 1, 105–110 (1954).
M. Bell, J. Ginsburg, and S. Todorcěvić, “Countable spread of exp Y and λY,” Topol. Appl.,14, No. 1, 1–12 (1982).
C. Bessaga, “Infinite-dimensional locally compact convex sets and the shapes of compacta,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,20, No. 2, 354–360 (1976).
C. Bessaga and A. Pelczyński, “Selected topics in infinite-dimensional topology,” Monogr. Mat. PAN,58, 353 (1975).
R. H. Bing, “Retractions onto ANRS,” Proc. Am. Math. Soc.,21, No. 3, 618–620 (1969).
C. R. Borgers, “A study of absolute extensor space,” Pac. J. Math.,31, No. 3, 609–617 (1969).
J. T. Borrego, Jr., “On Borsuk's paste job and related topics,” Doct. Diss. Univ. Fa., (1966), p. 104; Dissert. Abstrs.,B27, No. 5, 1535–1536 (1966).
K. Borsuk, “On some metrizations of the hyperspace of compact sets,” Fundam. Math.,41, No. 2, 168–202 (1955).
K. Borsuk, “On a concept of dependence for continuous mappings,” Fundam. Math.,43, No. 1, 95–113 (1956).
K. Borsuk, “Probleme der anschaulichen topologie,” Jahresber. Dtsch. Math,-Ver.,60, No. 3, 101–114 (1958).
K. Borsuk, “Concerning the classification of topological spaces from the standpoint of the theory of retracts,” Fundam. Math.,46, No. 3, 321–330 (1959).
K. Borsuk, “Theorie der retrakte und ihre Probleme,” Izv. Mat. Inst. Bulg. AN,4, 45–54 (1959).
K. Borsuk, “Sur l'élimination de phénoménes paradoxaus en topologie générale,” Proc. Internat. Congr. Math., Amsterdam, 1954; Vol. I, Groningen-Amsterdam (1957), pp. 197–208.
K. Borsuk, “Concerning the notion of R-neighbors,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,8, No. 7, 459–462 (1960).
K. Borsuk, “On a problem of V. Klee concerning the Hilbert manifolds,” Colloq. Math.,8, No. 2, 239–242 (1961).
K. Borsuk, “On AR-set with an infinite number of R-neighbors,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,9, No. 5, 345–349 (1961).
K. Borsuk, “Concerning the dimension of ANR-sets,” Bull. Acad. Polon. Sci. Sér. Sci. Math., Astron. Phys.,9, 685–687 (1961).
K. Borsuk, “Concerning the dimension of ANR-sets,” Gen. Topol. and Its Relat. Mod. Analysis and Algebra. Czechosl. Acad. Sci., 115–118 (1962).
K. Borsuk, “On a family of two-dimensional AR-sets,” Fundam. Math.,51, No. 3, 283–297 (1962).
K. Borsuk, “La théorie des rétractes,” Rend. Mat. Applic.,22, No. 1–2, 320–343 (1963).
K. Borsuk, “Concerning the set of retractions,” Colloq. Math.,18, 197–201 (1967).
K. Borsuk, “Theory of retracts,” Warszawa, PWN (1967), p. 251.
K. Borsuk, “On the shape of FANR-sets,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,17, No. 9, 529–532 (1969).
K. Borsuk, “Fundamental retracts and extensions of fundamental sequences,” Fundam. Math.,64, No. 1, 55–85 (1969).
K. Borsuk, “On nearly extendable maps,” Bull. Acad. Pol. Sci. Sér. Sci. Math. Astron., Phys.,23, No. 7, 753–760 (1975).
K. Borsuk, “On a class of compacta,” Houston J. Math.,1, No. 1, 1–13 (1975).
K. Borsuk and A. Kirkor, “Two remarks concerning retracts of ANR-spaces,” Colloq. Math.,17, No. 2, 325–326 (1967).
K. Borsuk and R. Molski, “On a class of continuous mappings,” Fundam. Math.,45, No. 1, 84–98 (1957).
H. G. Bothe, “Eine Einbettung m-dimensionaler Mengen in einen (m+1)-dimensionalen absoluten Retract,” Fundam. Math.,52, No. 2, 209–224 (1963).
R. Bott, “On the third symmetric potency of S1,” Fundam. Math., No. 3, 264–268 (1952).
D. G. Bourgin, “Un indice dei punti uniti. Nota I, II,” Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. Natur.,19 (20), No. 6 (No. 1), 435–440 (43–48) (1955) (1956).
D. G. Bourgin, “Un indice dei punti uniti. Nota. III,” Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. Natur.,21, No. 6, 395–400 (1956).
D. G. Bourgin, “Fixed points on neighborhood retracts,” Rev. Math. Pures Appl. (RPR),2, 371–374 (1957).
L. Boxer, “The space of ANRs of a closed surface,” Pac. J. Math.,79, No. 1, 47–68 (1978).
L. Boxer, “Retraction spaces and the homotopy metric,” Topol. Appl.,11, No. 1, 17–29 (1980).
L. Boxer, “Global properties of spaces of ARs,” Rocky Mount. J. Math.,10, No. 4, 665–669 (1980).
B. Brechner and E. Duda, “A characterization of monotone open retracts of a 2-cell,” Gen. Topol. Appl.,7, No. 1, 15–29 (1977).
D. Burghelea and D. Henderson, “Smoothings and homeomorphisms for Hilbert manifolds,” Bull. Am. Math. Soc.,76, No. 6, 1261–1265 (1970).
D. Burghelea and N. Kuiper, “Hilbert manifolds,” Ann. Math.,90, No. 3, 379–417 (1969).
C. E. Capel and W. L. Strother, “A space of subsets having the fixed point property,” Proc. Am. Math. Soc.,7, No. 4, 707–708 (1956).
H. Gartan, “Problémes d'homotopie et de prolongement; théorie des obstruction,” Sém. H. Cartan. École Norm. Supér.,2, No. 3, 1–10 (1949–1950) (1956); “Applications d'espaces localement compacts dans les polyédres: dimension, problémes d'homotopie et de prolongement,” Sem. H. Cartan. École Norm. Supér.,2, No. 4, 1–10 (1949–1950) (1956).
R. Cauty, “Sur le prolongement des fonctions continues á valeurs dans les CW-complexes,” C. R. Acad. Sci.,273, No. 25, A1208–A1211 (1971).
R. Cauty, “Sur le prolongement des fonctions continues á valeurs dans les CW-complexes,” C. R. Acad. Sci.,274, No. 1, A35–A37 (1972).
R. Cauty, “Une généralisation du théoréme de Borsuk-Whitehead-Hanner aux espaces stratifiables,” C. R. Acad. Sci.,275, No. 4, A271–A274 (1972).
R. Cauty, “Un contre-exemple concernant les rétractions dans les variétés non paracompactes,” Arch. Math.,24, No. 6, 661–662 (1973).
R. Cauty, “Retractions dans les espaces stratifiables,” Bull. Soc. Math. France,102, No. 2, 129–149 (1974).
R. Cauty, “Classifiant de Milnor et rétractes absolus de voisinage,” Arch. Math.,28 No. 6, 623–631 (1974).
Z. Cerin, “Ep-movable at infinity spaces, compact ANR divisors and property UVWn,” Publs. Inst. Math.,23, 53–65 (1978).
Z. Cerin, “Spaces of AANRs,” Proc. Am. Math. Soc.,83, No. 3, 609–615 (1981).
T. A. Chapman, “Four classes of separable metric infinite-dimensional manifolds,” Bull. Am. Math. Soc.,76, No. 2, 399–403 (1970).
T. A. Chapman, “Deficiency in finite-dimensional manifolds,” Rept. Math. Cent., ZW, No. 10, 12 (1970).
T. A. Chapman, “Hilbert cube manifolds,” Bull. Am. Math. Soc.,76, No. 6, 1326–1330 (1970).
T. A. Chapman, “Infinite deficiency in Fréchet manifolds,” Trans. Am. Math. Soc.,148, No. 1, 137–146 (1970).
T. A. Chapman, “Contractible Hilbert cube manifolds,” Proc. Am. Math. Soc.,35, No. 1, 254–258 (1972).
T. A. Chapman, “On the structure of Hilbert cube manifolds,” Compos. Math.,24, No. 3, 329–353 (1972).
T. A. Chapman, “Homotopic homeomorphisms of infinite-dimensional manifolds,” Compos. Math.,27, No. 2, 135–140 (1973).
T. A. Chapman, “Homeomorphisms of Hilbert cube manifolds,” Tran. Am. Math. Soc.,182, Aug., 227–239 (1973).
T. A. Chapman, “Surgery and handle straightening in Hilbert cube manifolds,” Pac. J. Math.,45, No. 1, 59–79 (1973).
T. A. Chapman, “Cell-like mappings of Hilbert cube manifolds: applications to simple homotopy theory,” Bull. Am. Math. Soc.,79, No. 6, 1286–1291 (1973).
T. A. Chapman, “Compact Hilbert cube manifolds and the invariance of Whitehead torsion,” Bull. Am. Math. Soc.,79, No. 1, 52–56 (1973).
T. A. Chapman, “Simple homotopy theory for compact Hilbert cube manifold factors,” Lect. Notes Math.,375, 53–63 (1974).
T. A. Chapman, “On the theory of Hilbert cube manifolds,” Lect. Notes. Math.,378, 101–107 (1974).
T. A. Chapman, “Locally flat imbeddings of Hilbert cubes are flat,” Fundam. Math.,87, No. 2, 183–193 (1975).
T. A. Chapman, “Cell-like mappings of Hilbert cube manifolds: solution of a handle problem,” Gen. Top. Appl.,5, No. 2, 123–145 (1975).
T. A. Chapman, “Concordances of noncompact Hilbert cube manifolds,” Pac. J. Math.,63, No. 1, 89–124 (1976).
T. A. Chapman, “Simple homotopy theory for ANRs,” Gen. Topol. Appl.,7, No. 2, 165–174 (1977).
T. A. Chapman and Steve Ferry, “Hurewicz fiber maps with ANR fibers,” Topology,16, No. 2, 131–143 (1977).
T. A. Chapman and Steve Ferry, “Fibering Hilbert cube manifolds over ANRs,” Compos. Math.,36, No. 1, 7–35 (1978).
T. A. Chapman and L. C. Siebenmann, “Finding a boundary for a Hilbert cube manifold,” Acta Math.,137, No. 3–4, 171–208 (1976).
T. A. Chapman and R. Y. T. Wong, “On homeomorphism of infinite dimensional bundles, II,” Trans. Am. Math. Soc.,191, 261–268 (1974).
T. A. Chapman and R. Y. T. Wong, “On homeomorphisms on infinite dimensional bundles,” Trans. Am. Math. Soc.,191, 269–276 (1974).
W. H. Chapman and R. Pol, “On the retract factorization property,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 2, 143–145 (1977).
W. C. Chewning, “Connectivity retracts of unicoherent Peano continua in Rn,” Fundam. Math.,75, No. 1, 25–27 (1972).
C. O. Christenson and R. P. Osborne, “Pointlike subsets of a manifold,” Pac. J. Math.,24, No. 3, 431–435 (1968).
M. H. Clapp, “A generalization of absolute neighborhood retracts,” Doct. Diss. Univ. Washington, 1968, p. 76; Dissert. Abstr.,B29, No. 7, 2520 (1969).
P. E. Conner, “Retraction properties of the orbit space of a compact topological transformation group,” Duke Math. J.,27, No. 3, 341–357 (1960).
C. H. Cook, “On continuous extensions,” Math. Ann.,176, No. 4, 302–304 (1968).
C. H. Cook and W. T. Ingram, “Obtaining AR-like continua as inverse limits with only two bonding maps,” Glas. Mat.,4, No. 2, 309–312 (1969).
D. W. Curtis, “Hyperspaces homeomorphic to Hilbert space,” Proc. Am. Math. Soc.,75, No. 1, 126–130 (1979).
D. W. Curtis, “Hyperspaces of Peano continua,” Math. Centre Tracts, Amsterdam, No. 115, 51–65 (1979).
D. W. Curtis, “Hyperspaces of noncompact metric spaces,” Compos. Math.,40, No. 2, 139–152 (1980).
D. W. Curtis and R. M. Schori, “2x and C(X) are homeomorphic to the Hilbert cube,” Bull. Am. Math. Soc.,80, No. 5, 927–931 (1974).
D. W. Curtis and R. M. Schori, “Hyperspaces of polyhedra are Hilbert cubes,” Fundam. Math.,99, No. 3, 189–197 (1978).
D. W. Curtis and Vo-Thanh-Liem, “Infinite products which are homeomorphic to Hilbert space,” Gen. Topol. Appl.,10, No. 1, 19–25 (1979).
M. L. Curtis, “Deformation-free continua,” Ann. Math.,57, No. 2, 231–247 (1953).
M. L. Curtis, “A note on monotone deformation-free mappings,” Proc. Am. Math. Soc.,5, No. 3, 437–438 (1954).
M. L. Curtis, “A note on Kosinski's spaces,” Fundam. Math.,46, No. 1, 25–27 (1958).
W. H. Cutler, “Negligible subsets of infinite-dimensional Fréchet manifolds,” Proc. Am. Math. Soc.,23, No. 3, 668–675 (1969).
W. H. Cutler, “Property Z and property Y sets in F-manifolds,” Fundam. Math.,78, No. 2, 163–167 (1973).
J. Czipszer and L. Geher, “Extensions of functions satisfying a Lipschits condition,” Acta Math. Acad. Sci. Hung.,6, No. 1–2, 213–220 (1955).
F. A. Del, “Sugli spazi G-ANR,” Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat., Natur.,58, No. 5, 723–728 (1975).
A. Deleanu, “Un théoréme de point fixe pour les rétractes des espaces convexoides,” C. R. Acad. Sci.,247, No. 22, 1950–1952 (1958).
A. Deleanu, “Théories des points fixes sur les rétractes de voisinage des espaces convexoides,” Bull. Soc. Math. France,87, No. 3, 235–243 (1959).
A. Deleanu, “Une generalisation du théoréme du points fixe de Schauder,” Bull. Soc. Math. France,89, No. 2, 223–226 (1961).
A. Deleanu, “On a certain property of absolute neighborhood retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,10, No. 4, 199–200 (1962).
T. Dobrowolski and H. Torunczyk, “Separable complete ANRs admitting a group structure are Hilbert manifolds,” Topol. Appl.,12, No. 3, 229–235 (1982).
C. Dorsett, “Local connectedness in hyperspaces,” Rend. Circ. Mat. Palermo,31, No. 1, 137–144 (1982).
C. Dorsett, “Connectedness in hyperspaces,” J. Natur. Sci. Math.,22., No. 1, 61–70 (1982).
E. K. van Douwen, “Retractions from βX onto βX\X,” Gen. Topol. Appl.,9, No. 2, 169–173 (1978).
E. K. van Douwen, “Retracts of the Sorgenfrey line,” Compos. Math.,38, No. 2, 155–161 (1979).
C. H. Dowker, “Homotopy extension theorems,” Proc. London Math. Soc.,6, No. 21, 100–116 (1956).
C. H. Dowker, “Imbedding of metric complexes,” Algebr. Geometry and Topol., Princeton, N.J., Univ. Press (1957), pp. 239–242.
J. S. Downing, “Absolute retracts and extensors for nonnormal spaces,” Gen. Topol. Appl.,7, No. 3, 275–281 (1977).
P. H. Doyle, “Neighborhood deformation retraction in manifolds,” Portug. Math.,26, No. 3–4, 273–274 (1967).
R. Duda, “On compactification of absolute retracts,” Colloq. Math.,12, No. 1, 1–5 (1964).
J. Dugundji, “Absolute neighborhood retracts and local connectedness in arbitrary metric spaces,” Compos. Math.,13, No. 3, 229–246 (1958).
J. Uugundji, “Continuous mappings into nonsimple spaces,” Trans. Arn. Math. Soc.,86, No. 1, 256–268 (1957).
J. Dugundji, “Locally equiconnected spaces and absolute neighborhood retracts,” Fundam. Math.,57, No. 2, 187–193 (1965).
P. F. Duvall, Jr., “Neighborhoods of 1-connected ANRs in high dimensional piecewise, linear manifolds,” Doct. Diss., Yale Univ.,1967, p. 88. Dissert. Abstrs.,B28, No. 10, 4195–4196 (1968).
J. Dydak, “An algebraic condition characterizing FANR-spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,24, No. 7, 501–503 (1976).
J. Dydak, “A simple proof that pointed FANR-spaces are regular fundamental retracts of ANRs,” Bull. Acad. Pol. Sci. Sér. Math., Astron. Phys.,25, No. 1, 55–62 (1977).
J. Dydak, S. Nowak, and M. Strok, “On the union of two FANR-sets,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,24, No. 7, 485–489 (1976).
J. Dydak and M. Orlowski, “On the sum theorem for FANR-spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 2, 161–163 (1977).
J. Dydak and A. Trybulec, “On regularly movable compacta,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,23, No. 8, 907–909 (1975).
C. Eberhart, “Intervals of continua which are Hilbert cubes,” Proc. Am. Math. Soc.,68, No. 2, 220–224 (1978).
G. Eberhart and Sam B. Nadler, Jr., “Hyperspaces of cones and fans,” Proc. Am. Math. Soc.,77, No. 2, 279–288 (1979).
C. Eberhart, Sam B. Nadler, Jr., and W. O. Nowell, Jr., “Spaces of order arcs in hyperspaces,” Fundam. Math.,112, No. 2, 111–120 (1981).
B. Eckmann, “Räume mit Mittelbildungen,” Comment. Math. Helv.,28, No. 4, 329–340 (1954).
D. A. Edwards and R. Geoghegan, “Infinite-dimensional Whitehead and Vietoris theorems in shape and prohomotopy,” Trans. Am. Math. Soc.,219, 351–360 (1976).
R. D. Edwards, “The topology of manifolds and cell-like maps,” Proc. Int. Congr. Math., Helsinki, Aug. 15–23, 1978, Vol. 1, Helsinki (1980), pp. 111–127
R. D. Edwards, “Characterizing infinite-dimensional manifolds topologically,” Lect. Notes Math.,770, 278–302 (1980).
R. Engelking, R. W. Heath, and E. Michael, “Topological well-ordering and continuous selections,” Invent. Math.,6, No. 2, 150–158 (1968).
E. R. Fadell, “A property of compact absolute neighborhood retracts,” Duke Math. J.,22, No. 2, 179–184 (1955).
E. R. Fadell, “A note on the nonexistence of strongly homogeneous ARs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,12, No. 9, 531–534 (1964).
A. Fathi, A. Marin, and Y. M. Visetti, “New proofs of Chapman's CE mapping theorem and West's mapping cylinder theorem,” Proc. Am. Math. Soc.,67, No. 2, 327–334 (1977).
A. Fathi and Y. M. Visetti, “A reduction of the fundamental conjecture about locally compact ANRs,” Proc. Am. Math. Soc.,49, No. 2, 446–448 (1975).
A. Fathi and Y. M. Visetti, “Deformation of open embeddings of Q-manifolds,” Trans. Am. Math. Soc.,224, No. 2, 427–435 (1976).
V. V. Fedorchuk, “Absolute retracts and some functors,” Gen. Topol. Relat. Mod. Anal. Algebra 5, Berlin, 174–182 (1983).
S. Ferry, “The homeomorphism group of a compact Q-manifold is an ANR,” Bull. Am. Math. Soc.,82, No. 6, 910–912 (1976).
S. Ferry, “The homeomorphism group of a compact Hilbert cube manifold is an ANR,” Ann. Math.,106, No. 1, 101–119 (1977).
S. Ferry, “Strongly regular mappings with compact ANR fibers are Hurewicz fiberings,” Pac. J. Math.,75, No. 2, 373–382 (1978).
E. E. Floyd, “Orbit spaces of finite transformation groups. I,” Duke Math. J.,20, No. 4, 563–567 (1953).
E. E. Floyd, “Orbit spaces of finite transformation groups. II,” Duke Math. J.,22, No. 1, 33–38 (1955).
E. E. Floyd and M. K. Fort, Jr., “A characterization theorem for monotone mappings,” Proc. Am. Math. Soc.,4, No. 5, 828–830 (1953).
M. K. Fort, Jr., “Extensions of mappings into n-cubes,” Proc. Am. Math. Soc.,7, No. 3, 539–542 (1956).
L. F. Foulis, “Subsets of an absolute retract,” Proc. Am. Math. Soc.,8, No. 2, 365–366 (1957).
J. Foutanillas, “Un teorema de seleccion uniforme,” Rev. Mat. Hisp.-Am.,37, No. 1–2, 3–18 (1977).
T. Ganea, “Remark on R-equivalent spaces,” Acta Math. Acad. Sci. Hung.,3, No. 4, 293–297 (1952).
T. Ganea, “Contractibilitatea produselor simetrice,” Studii Si Cerc. Mat.,4, No. 1–2, 23–28 (1953).
T. Ganea, “Symmetrische Potenzen topologis cher Räume,” Math. Nachr.,11, No. 4–5, 305–316 (1954).
T. Ganea, “Produse simetrice de spatii topologice,” Commun. Acad. R. P., Romine,4, No. 11, 561–563 (1954).
B. D. Garrett, “Almost continuous retracts,” Gen. Topol. Mod. Anal. Proc. Conf., Riverside, Calif., May 28–31, 1980, New York (1981), pp. 229–238.
G. Gauthier, “Fixed point theorems for approximative ANRs,” Lect. Notes Math.,886, 103–115 (1981).
R. Geoghegan, “On spaces of homeomorphisms embeddings and functions, I,” Topology,11, No. 2, 159–177 (1972).
R. Geoghegan, “Hilbert cube manifolds of maps,” Gen. Topol. Appl.,6, No. 1, 27–35 (1976).
F. Gherardelli, “Progressi recenti nella teoria delle varitetá differenziabili di dimensione infinita,” Boll. Unione Mat. Ital.,1, No. 2, 207–218 (1968).
A. Gmurczyk, “On approximative retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,16, No. 1, 9–14 (1986).
S. Godlewski, “Some remarks concerning the mappings of the inverse limit into an absolute neighborhood retract and its applications to cohomotopy groups,” Fundam. Math.,63, No. 1, 89–95 (1968).
S. Godlewski, “A characterization of MAR and MANR-spaces by extendability of mutations,” Fundam. Math.,89, No. 3, 229–232 (1975).
A. J. Goldman, “Metric extension,” Pi Mu Epsilon J.,1, No. 10, 400–406 (1954).
J. T. Goodykoontz, Jr., “C(X) is not necessarily a retract of 2x,” Proc. Am. Math. Soc.,67, No. 1, 177–178 (1977).
J. T. Goodykoontz, Jr., “Hyperspaces of arc-smooth continua,” Houston J. Math.,7, No. 1, 33–41 (1981).
J. T. Goodykoontz, Jr., “Arc-smoothness in hyperspaces,” Topol. Appl.,15, No. 2, 131–150 (1983).
G. R. Gordh, Jr., “On inverse limits of ANRs with metric shape,” Math. Balkan, No. 4, 225–228 (1974).
G. R. Gordh, Jr., “Every continuum is a retract of some irreducible indecomposable continuum,” Topics Topology, Amsterdam-London, 347–350 (1974).
L. Górniewicz, “Repulsywne punkty stale zwartych odwzorowan topologicznie zupellnych ANR-ów,” Zesz. Nauk. UG. Matematyka, No. 3, 57–66 (1976).
A. Granas, “Fixed point theorems for approximative ANRs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,16, No. 1, 15–19 (1968).
N. Gray, “A new characterization of AR(\(\mathfrak{M}\)) and ANR(\(\mathfrak{M}\)),” Bull. Am. Math. Soc.,75, No. 3, 607–609 (1969).
J. deGroot, “On some problems of Borsuk concerning a hyperspace of compact sets,” Proc. Koninkl. Nederl. Akad. Wetensch.,A59, No. 1, 95–103 (1959), Indag. Math.,18, No. 1, 95–103 (1956).
M. Gutierrez-Burzaco, “Extension of uniform homotopies,” Proc. Koninkl. Nederl. Akad. Wet.,A11, No. 1, 61–69 (1958).
M. Handel, “On certain sums of Hilbert cubes,” Gen. Topol. Appl.,9, No. 1, 19–28 (1978).
M. Handel, “The Bing staircase construction for Hilbert cube manifolds,” Gen. Topol. Appl.,9, No. 1, 29–40 (1978).
O. Hanner, “Some theorems on absolute neighborhood retracts,” Ark. Mat.,1, No. 5, 389–408 (1951).
O. Hanner, “Retraction of metric and non-metric spaces,” Proc. Internat. Congr. Math., 2 (1954), Amsterdam, 227 (1954).
M. Hasumi, “A continuous selection theorem for extremely disconnected spaces,” Math. Ann.,179, No. 2, 83–89 (1969).
W. Haver, “Mappings between ANRs that are fine homotopy equivalences,” Pac. J. Math.,58, No. 2, 457–461 (1975).
R. Heisey, “Manifolds modeled on R∞ or bounded weak*-topologies,” Trans. Am. Math. Soc.,206, 295–312 (1975).
R. Heisey, “A factorization of the direct limit of Hilbert cubes,” Proc. Am. Math. Soc.,54, 255–260 (1976).
R. Heisey, “Stability, open embeddings and classification of bounded weak-manifolds,” Gen Topol. Appl.,6, No. 3, 327–338 (1976).
R. Heisey and H. Torunczyk, “On the topology of direct limits of ANRs,” Pac. J. Math.,93, No. 2, 307–312 (1981).
D. W. Henderson, “Infinite-dimensional manifolds are open subsets of Hilbert space,” Bull. Am. Math. Soc.,75, No. 4, 759–762 (1969).
D. W. Henderson, “Infinite-dimensional manifolds,” Proc. Int. Symp. Topol. Its Appl., Herceg-Novi (1968), Beograd (1969), pp. 183–185.
D. W. Henderson, “Infinite-dimensional manifolds are open subsets of Hilbert space,” Topology,9, No. 1, 25–33 (1970).
D. W. Henderson, “Negligible subsets of infinite-dimensional manifolds,” Proc. Int. Symp. Topol. Its Appl., Herceg-Novi (1968), Beograd (1969), p. 186.
D. W. Henderson, “Applications of infinite-dimensional manifolds to quotient spaces of complete ANRs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,19, No. 8, 747–753 (1971).
D. W. Henderson, “A simplicial complex whose product with any ANR is a simplicial complex,” Gen. Topol. Appl.,3, No. 1, 81–83 (1973).
D. W. Henderson, “Z-sets in ANRs,” Trans. Am. Math. Soc.,213, 205–216 (1975).
D. W. Henderson and R. Schori, “Topological classification of infinite-dimensional manifolds by homotype,” Bull. Am. Math. Soc.,76, No. 1, 121–129 (1970).
D. W. Henderson and J. E. West, “Triangulated infinite-dimensional manifolds,” Bull. Am. Math. Soc.,76, No. 3, 655–660 (1970).
S. K. Hildebrand and D. E. Sanderson, “Connectivity functions and retracts,” Fundam. Math.,57, No. 3, 237–245 (1965).
J. G. Hollingsworth, “Homotopy types of compact ANRs,” Doct. Diss. Rice Univ., 1967, p. 50. Dissert. Abstrs.,B28, No. 4, 1612–1613 (1967).
C. J. Houghton, “Retraction onto a dendrite,” Duke Math. J.,33, No. 4, 673–677 (1966).
Sze-Tsen Hu, “Theory of retracts,” Wayne State Univ. Press, Detroit (1965), p. 234.
L. S. Husch, “Intersections of ANRs,” Fundam. Math.,104, No. 1, 21–26 (1979).
D. M. Hyman, “Quotient spaces of absolute neighborhood retracts,” Doct. Diss. Univ. Md., 1966, p. 88. Dissert. Abstrs.,B27, No. 9, 3185 (1967).
D. M. Hyman, “A generalization of the Borsuk-Whitehead-Hanner theorem,” Pac. J. Math.,23, No. 2, 263–271 (1967).
D. M. Hyman, “ANR divisors and absolute neighborhood contractibility,” Fundam. Math.,62, No. 1, 61–73 (1968).
D. M. Hyman, “On decreasing sequences of compact absolute retracts,” Fundam. Math.,64, No. 1, 91–97 (1969).
Kiyoshi Iséki, “On hannerisation of two countable paracompact normal spaces,” Proc. Jpn. Acad.,30, No. 6, 443–444 (1954).
Kiyoshi Iséki, “On a property of mappings of metric spaces,” Proc. Jpn. Acad.,30, No. 7, 570–571 (1954).
Kiyoshi Iseki, “On extension of continuous mappings on countable paracompact normal spaces,” Proc. Jpn. Acad.,30, No. 8, 736–740 (1954).
Kiyoshi Iséki, “Some properties of hypernormal spaces,” Proc. Jpn. Acad.,30, No. 10, 937–939 (1954).
Kiyoshi Iseki, “A note on retraction in completely normal spaces,” Rev. Fac. Ci., Univ. Lisboa,A3, 176–180 (1954).
G. J. O. Jameson, “An elementary proof of the Arens and Borsuk extension theorems,” J. London Math. Soc.,14, No. 2, 364–368 (1976).
An. Jankowski, “Les applications d'opérations homotopiques au problémes due prolongement,” C. R. Acad. Sci.,264, No. 7, A315–A318 (1967).
J. Jarón, “On the extensibility of mappings, their local properties and some of their connections with the dimension theory,” Fundam. Math.,48, No. 3, 287–305 (1960).
J. W. Jaworowski, “Some remarks on Borsuk generalized cohomotopy groups,” Fundam. Math.,50, No. 3, 257–264 (1962).
J. W. Jaworowski, “Generalized cohomotopy groups as limit groups,” Fundam. Math.,50, No. 4, 393–402 (1962).
J. W. Jaworowski, “Symmetric products of ANRs,” Math. Ann.,192, No. 3, 173–176 (1971).
J. W. Jaworowski, “Extensions of maps in space with periodic homeomorphisms,” Bull. Am. Math. Soc.,78, No. 4, 527–531 (1972).
J. W. Jaworowski, “Symmetric products of ANRs associated with a permutation group,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,20, No. 8, 649–651 (1972).
A. Kadlof, “On Borsuk's conjecture concerning the characterization of FANRs,” Glas. Math.,16, No. 2, 377–380 (1981).
Tetsuo Kando, “Characterization of topological spaces by some continuous functions,” J. Math. Soc. Jpn.,6, No. 1, 45–54 (1954).
Hisao Kato, “Strongly regular mappings with ANR fibers and shape,” J. Math. Soc. Jpn.,35, No. 2, 243–249 (1983).
J. Keesling and D. C. Wilson, “The group of PL-homeomorphism of a compact PL-manifold is anl 2 f-manifold,” Trans. Am. Math. Soc.,193, No. 466, 249–256 (1974).
J. Keesling, “A nonmovable trivial-shape decomposition of the Hilbert cube,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,23, No. 9, 997–998 (1975).
K. Kellum, “On a question of Borsuk concerning noncontinuous retracts. I,” Fundam. Math.,87, No. 2, 89092 (1975).
K. Kellum, “Noncontinuous retracts,” Stud. Topol., New York, 255–261 (1975).
K. Kellum, “On a question of Borsuk concerning noncontinuous retracts. II,” Fundam. Math.,92, No. 2, 135–140 (1976).
K. Kellum, “The equivalence of absolute almost continuous retracts and ɛ-absolute retracts,” Fundam. Math.,96, No. 3, 229–235 (1977).
Shin-ichi Kinoshita, “On some contractible continua without fixed point property,” Fundam. Math.,40, 96–98 (1953).
J. M. Kister, “Homotopy types of ANRs,” Proc. Am. Math. Soc.,19, No. 1, 195 (1968).
B. Knaster and M. Reichbach, “Notion d'homogénéite et prolongements des homéomorphies,” Fundam. Math.,40, 180–193 (1953).
Yukihiro Kodama, “Mappings of a fully normal space into an absolute neighborhood retract,” Sci. Rept. Tokyo Kyoiku Daigaku,A5, 37–47 (1955).
Yukihiro Kodama, “On LCn metric spaces,” Proc. Jpn. Acad.,33, No. 2, 79–83 (1957).
Yukihiro Kodama, “Note on an absolute neighborhood extensor for metric spaces,” J. Math. Soc. Jpn.,8, No. 3, 206–215 (1956).
Yukihiro Kodama, “On sum theorems of ANR and a characteristic property of completely collectionwise normal spaces,” Sci. Repts. Tokyo Kyoiku Diagaku,A5, Feb. (1956), pp. 122–129.
Yukihiro Kodama, “On ANR for metric spaces,” Sci. Repts. Tokyo Kyoiku Diagaku,A5, Nov. (1955), pp. 96–98.
Yukihiro Kodama, “On a closed mapping between ANRs,” Fundam. Math.,45, No. 3, 217–227 (1958).
Yukihiro Kodama, “On embeddings of spaces into ANR and shapes,” J. Math. Soc. Jpn.,27, No. 4, 533–544 (1975).
Yukihiro Kodama, “A remark on the union of pointed FANRs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,26, No. 3, 255–260 (1978).
Yukihiro Kodama, “A characteristic property of a finite dimensional pointed FANR,” Jpn. J. Math. New Ser.,4, No. 2, 445–460 (1978).
Yukihiro Kodama, “On noncompact FANRs and MANRs,” Fundam. Math.,115, No. 3, 223–227 (1983).
A. Kosiński, “On manifolds and r-spaces,” Fundam. Math.,42, No. 1, 111–124 (1955).
A. Kosiński, “A note on the labil points,” Golloq. Math.,4, No. 1, 11–12 (1956).
A. Kosiński, “Some theorems about two-dimensional polyhedra,” Fundam. Math.,47, No. 1, 1–28 (1959).
G. Kozlowski, “Maps of ANRs determined on null sequences of ARs,” Stud. Topol., New York, 277–284 (1975).
G. Kozlowski, J. van Mill, and J. J. Walsh, “AR-maps obtained from cell-like maps,” Proc. Am. Math. Soc.,82, No. 2, 299–302 (1981).
Akira Koyama, “Various compact multiretracts and shape theory,” Tsukuba J. Math.,6, No. 2, 319–332 (1982).
J. Krasinkiewicz, “On a method of constructing ANR-sets. On application of inverse limits,” Fundam. Math.,92, No. 2, 95–112 (1976).
N. Kroonenberg, “Pseudointeriors of hyperspaces,” Compos. Math.,32, No. 2, 113–131 (1976).
A. H. Kruse, “Local deformation retractions,” Math. Z.,116, No. 3, 264–270 (1970).
A. H. Kruse and P. W. Liebnitz, “An application of a family homotopy extension theorem to ANR spaces,” Pac. J. Math.,16, No. 2, 331–336 (1966).
W. Kuperberg and J. Oledzki, “On certain types of movability of the approximately k-connected compacta,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 11, 1171–1173 (1977).
K. Kuratowski, “Sur une méthode de métrisation compléte de certains espaces d'ensebles compacts,” Fundam. Math.,43, No. 1, 114–138 (1956).
K. Kuratowski, “Quelques propriétés de l'espace des ensebles LCn,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys., Cl.3, 5, No. 10, 967–974 (1957).
K. Kuratowski, “Sur les composantes de l'espace des transformations d'un espace localement compact en un rétracte de voisinage,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,6, No. 9, 565–571 (1958).
K. Kuratowski, “On discontinuous selectors,” Gen. Topol. Relat. Mod. Anal. Algebra, Vol. 2, Prague, 235 (1967).
K. Kuratowski and C. Ryll-Nardzewski, “A general theorem on selectors,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,13, No. 6, 397–403 (1965).
S. Kwasik, “A Lefschetz-type fixed point theorem for absolute neighborhood retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 9, 885–889 (1977).
R. C. Lacher, “Cell-like mapping of ANRs,” Bull. Am. Math. Soc.,74, No. 5, 933–935 (1968).
A. Y. W. Lau and C. H. Voas, “Connections of the hyperspace of closed connected subsets,” Rocz. Pol. Tow. Mat., Ser. I,20, No. 2, 393–396 (1978).
J. D. Lawson, “Applications of topological algebra to hyperspace problems,” Topology, New York-Basel (1976), pp. 201–206.
A. Lelek, “Some mappings of ANR-sets,” Fundam. Math.,52, No. 2, 225–233 (1963).
P. W. Liebnitz, Jr., “Neighborhood extensions of continuous maps,” J. Reine Angew. Math.,222, No. 1–2, 58–68 (1966).
I. Lončar and S. Mardešić, “A note on inverse sequences of ANRs,” Glas. Mat.,3, No. 1, 41–48 (1968).
M. Lubański, “An example of an absolute neighborhood retract, which is the common boundary of three regions in the three-dimensional Euclidean space,” Fundam. Math.,40, No. 1, 29–38 (1953).
L. Lum, “A characterization of local connectivity in dendroids,” Stud. Topol., New York, 331–338 (1975).
J. Luukkainen, “Extensions of spaces, maps, and metrics in Lipschitz topology,” Ann. Acad. Sci. Fenn., Ser.A1, Diss., No. 17, 62 (1978).
J. M. Lysko, “On AR-spaces with small homeomorphism group,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,22, No. 7, 679–681 (1974).
J. M. Lysko, “Some theorems concerning finite dimensional homogeneous ANR-spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,24, No. 7, 491–496 (1976).
T. Maćkowiak, “Continuous selections for C(X),” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,26, No. 6, 547–551 (1978).
V. J. Mancuso, “Retracts and extension spaces for certain classes on normal spaces,” Doct. Diss., Rutgers State Univ., 1966, p. 51. Dissert. Abstrs.,B27, No. 1, 230 (1966).
V. J. Mancuso, “Retraction in m-paracompact spaces,” Proc. Am. Math. Soc.,18, No. 6, 1080–1083 (1967).
V. J. Mancuso, “n-ANRs for certain normal spaces,” Can. J. Math.,19, No. 3, 629–635 (1967).
S. Mardešić, “Equivalence of singular and Cech homology for absolute neighborhood retracts. Application to unicoherence,” Fundam. Math.,46, No. 1, 29–45 (1958).
S. Mardešić and J. Segal, “Movable compacta and ANR-systems,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,18, No. 11, 649–654 (1970).
S. Mardešić and A. P. Sostak, “On the homotopy type of ANRs for p-paracompacta,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,27, No. 10, 803–808 (1979).
J. R. Martin, “A generalization of absolute retracts,” Proc. Am. Math. Soc.,52, 409–413 (1975).
J. R. Martin, “An example of a contractible LC∞ compactum which is not an absolute approximate retract,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 5, 489–492 (1977).
J. R. Martin, “Absolute fixed-point sets in compacts,” Colloq. Math.,39, No. 1, 41–44 (1978).
J. R. Martin, “Absolute approximate retracts and AR-spaces,” Can. J. Math.,33, No. 2, 297–301 (1981).
J. R. Martin, “Absolute fixed point sets and AR-spaces,” Fundam. Math.,112, No. 2, 159–164 (1981).
W. K. Mason, “The space of all self-homeomorphisms of a two-cell which fix the cells boundary is an absolute retract,” Trans. Am. Math. Soc.,161, 185–205 (1971).
G. P. Massaro, “Quelques questions préalables á propos du probléme des sélections, en rapport avec celui des fonctions implicites,” C. R. Acad. Sci.,244, No. 2, 153–155 (1957).
G. P. Massaro, “Constructions á propos du probléme des sélections,” C. R. Acad. Sci.,244, No. 3, 294–297 (1957).
J. H. McAlpin, “Infinite dimensional manifolds and Morse theory,” Doct. Diss., Columbia Univ., 1965, p. 119. Dissert. Abstrs.,26, No. 8 (1966).
B. H. McCandless, “Test spaces for dimension n,” Proc. Am. Math. Soc.,7, No. 6, 1126–1130 (1956).
B. H. McCandless, “Test spaces for metric spaces,” Proc. Am. Math. Soc.,10, No. 3, 372–376 (1959).
B. H. McCandless, “Test spaces for normal spaces,” Proc. Am. Math. Soc.,13, No. 4, 514–517 (1962).
B. H. McCandless, “Retracts and extension spaces for perfectly normal spaces,” Michigan Math J.,9, No. 3, 193–197 (1962).
B. H. McCandless, “Retracts and extension spaces for perfectly normal spaces. II,” Portug. Math.,22, No. 3–4, 205–207 (1963).
B. H. McCandless, “Perfect normality, local neighborhood extension spaces, and contractibility of absolute retracts,” Math. Z.,85, No. 5, 385–391 (1964).
B. H. McCandless, “On a theorem of Hanner and Dowker,” Portug. Math.,26, No. 3–4, 479–482 (1967).
M. M. McWaters and J. H. Reed, “Retractions and quasimonotone mappings of unicoherent spaces,” Proc. Am. Math. Soc.,33, No. 2, 557–561 (1972).
E. Michael, “Some extension theorems for continuous functions,” Pac. J. Math.,3, No. 4, 789–806 (1953).
E. Michael, “Local properties of topological spaces,” Duke Math. J.,21, No. 1, 163–171 (1954).
E. Michael, “Selection theorems for continuous functions,” Proc. Internat. Congr. Math., Amsterdam,2, 241–242 (1954).
E. Michael, “Continuous selections. I,” Ann. Math.,63, No. 2, 361–382 (1956).
E. Michael, “Continuous selections. II,” Ann. Math.,64, No. 3, 562–580 (1956).
E. Michael, “Continuous selections. III,” Ann. Math.,65, No. 2, 375–390 (1957).
E. Michael, “Selected selection theorems,” Am. Math. Monthly,63, No. 4, 233–238 (1956).
E. Michael, “Uniform ARs and ANRs,” Compos. Math.,39, No. 2, 129–139 (1979).
E. Michael, “Some results on continuous selections,” Math. Centre Tracts, Amsterdam, No. 115, 161–163 (1979).
E. Michael, “Continuous selections: some old and some new results,” Topo. 4th Colloq., Vol. 2, Budapest (1978), Amsterdam (1980), pp. 849–851.
E. Michael, “Continuous selections and countable sets,” Fundam. Math.,111, No. 1, 1–10 (1981).
M. Michael, “Some hyperspaces homeomorphic to separable Hilbert space,” Gen. Topol. Mod. Anal. Proc. Conf., Riverside, Calif., May 28–31, 1980, New York (1981), pp. 291–294.
J. van Mill, “The superextension of the closed unit interval is homeomorphic to the Hilbert cube,” Fundam. Math.,103, No. 3, 151–175 (1979).
J. van Mill, “Superextensions of metrizable continua are Hilbert cubes,” Fundam. Math.,107, No. 3,201, 224 (1980).
J. van Mill, “A rigid space X for which X×X is homogeneous, an application of infinite dimensional topology,” Proc. Am. Math. Soc.,83, No. 3, 597–600 (1981).
J. van Mill, “A counterexample in ANR theory,” Topol. Appl.,12, No. 3, 315–320 (1981).
J. van Mill and Marcel van de Vel, “On an internal property of absolute retracts,” Topol. Appl.,13, No. 1, 59–68 (1982).
R. T. Miller, “Mapping cylinder neighborhoods of some ANRs,” Bull. Am. Math. Soc.,81, No. 1, 187–188 (1975).
R. T. Miller, “Mapping cylinder neighborhoods of some ANRs,” Ann. Math.,103, No. 2, 417–427 (1976).
W. J. R. Mitchell, “General position properties of ANRs,” Math. Proc. Cambrige Philos. Soc.,92, No. 3, 451–466 (1982).
Katuhiko Mizuno, “On homotopy classification and extension,” J. Inst. Polytech. Osaka Univ.,A6, No. 2, 55–69 (1955).
G. Mokobodzki, “Sélections continues (d'aprés Ernest Michael),” Sem. Choquet., 1963, 2 (1964).
R. Molski, “On symmetric products,” Fundam. Math.,44, No. 2, 165–170 (1957).
R. Molski, “On an irreducible absolute retract,” Fundam. Math.,57, No. 2, 121–133 (1965).
R. Molski, “On a family of AR-sets,” Fundam. Math.,57, No. 2, 135–145 (1965).
D. A. Moran, “The minimum dimension of a residual ANR,” Colloq. Math.,36, No. 1, 97–99 (1976).
F. Morel, “Cohomologie singuliére et cohomologie des Q-variétès,” C. R. Acad. Sci.,281, No. 10, A309–A312 (1975).
F. Morel, “Type d'homotopie rationnelle des Q-variétès et formes simpliciales basiques,” C. R. Acad. Sci.,A285, No. 1, B285, No. 1, A11–A14 (1977).
K. Morita and T. Hoshina, “C-embedding and the homotopy extension property,” Gen. Topol. Appl.,5, No. 1, 69–81 (1975).
M. Morse, “A reduction of the Shoenflies extension problem,” Bull. Am. Math. Soc.,66, No. 2, 113–115 (1960).
M. Moszynska, “Generalization of the theory of retracts on the pairs of spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,13, No. 1, 13–19 (1965).
M. Moszynska, “ANR-spaces, which are deformation retracts of some polyhedra,” Fundam. Math.,66, No. 1, 203–214 (1970).
K. K. Mukherjea, “Coincidence theory for infinite dimensional manifolds,” Bull. Am. Math. Soc.,74, No. 3, 493–496 (1968).
S. B. Nadler, Jr., “A characterization of locally connected continua by hyperspace retractions,” Proc. Am. Math. Soc.,67, No. 1, 167–176 (1977).
S. B. Nadler, Jr., “Hyperspaces of sets. A text with research questions,” New York-Basel, Marcel Dekker (1978), p. 708.
S. B. Nadler, Jr., J. E. Quinn, E. Joseph, and N. M. Stavrakas, “Hyperspaces of compact convex sets. II,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,25, No. 4, 381–385 (1977).
S. B. Nadler, Jr., J. Quinn, and Nick M. Stavrakas, “Hyperspaces of compact convex sets,” Pac. J. Math.,83, No. 2, 441–462 (1979).
Keiô Nagami, “On some types of polyhedra,” Proc. Jpn. Acad.,32, No. 4, 245–247 (1956).
Minoru Nakaoka, “Gohomology of the three-fold symmetric products of spheres,” Pac. J. Math.,31, No. 10, 670–671 (1955).
G. Nepomnjaščii, “A spectral characterization of absolute multivalued retracts,” Gen. Topol. Relat. Mod. Anal. Algebra 5, Berlin, 507–510 (1983).
L. S. Newman, “Applications of group actions on finite complexes to Hilbert cube manifolds,” Proc. Am. Math. Soc.,62, No. 1, 183–187 (1977).
Togo Nishiura and Choon Jai Rhee, “Contractibility of the hyperspace of subcontinua,” Houston J. Math.,8, No. 1, 119–127 (1982).
W. Nitka, “Une generalization du theoreme de Kuretowski sur la caractérisation métrique de la rétraction,” Colloq. Math.,8, No. 1, 35–37 (1961).
Hiroshi Nogushi, “A generalization of absolute neighborhood retracts,” Kodai Math. Sem. Repts., No. 1, 20–22 (1953).
R. D. Nussbaum, “Some generalization of the Borsuk-Ulam theorem,” Proc. London Math. Soc.,35, No. 1, 136–158 (1977).
H. Oike and Y. Kuriyama, “On the retractions of stunted projective spaces,” Tohoku Math. J.,19, No. 4, 454–461 (1967).
R. C. O'Neill, “Retracts and retractile subcomplexes,” Topology,5, No. 2, 191–201 (1966).
L. G. Oversteegen, “Open retractions and locally confluent mappings of certain continua,” Houston J. Math.,6, No. 1, 113–125 (1980).
H. Patkowska, “On the decomposition of two-dimensional ANRs into a Cartesian product,” Fundam. Math.,52, No. 1, 13–23 (1963).
H. Patkowska, “On the uniqueness of the decomposition of finite dimensional ANRs into Cartesian products of at most one-dimensional spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,13, No. 1, 7–12 (1965).
H. Patkowska, “Some theorems on the embeddability of ANR-spaces into Euclidean spaces,” Fundam. Math.,65, No. 3, 289–308 (1969).
H. Patkowska, “Some theorems about the embeddability of ANR-sets into decomposition spaces of En,” Fundam. Math.,70, No. 3, 271–306 (1971).
P. R. Patten, “Refinable maps and generalized absolute neighborhood retracts,” Topol. Appl.,14, No. 2, 183–188 (1982).
M. Pavel, “Clasele de homotopie ale transformăarilor eqal continue,” Commun. Acad. R. P. Romane,3, No. 3–4, 115–116 (1953).
M. Pavel, “Unele proprietăati ale retractelor liniare,” An. Univ. C. I. Parhon. Ser. Stiint. Natur., No. 10, 19–22 (1956).
A. Pelcar, “On some extensions of the retract theorem of T. Ważewski,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,17, No. 11, 693–698 (1969).
A. Pelcar, “On some extensions of the retract theorem of T. Ważewski. II,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,18, No. 11, 641–647 (1970).
A. Petrus, “Contractibility of Whitney continua in C(X),” Gen. Topol. Appl.,9, No. 3, 275–288 (1978).
C. P. Pixley, “Continuously choosing a retraction of a separable metric space onto each of its arcs,” III. J. Math.,20, No. 1, 22–29 (1976).
T. Przymusinski, “Collectionwise normality and absolute retracts,” Fundam. Math.,98, No. 1, 61–73 (1978).
J. Quinn and R. Y. T. Wong, “Union of convex Hilbert cubes,” Proc. Am. Math. Soc.,65, No. 1, 171–176 (1972).
C. E. Robinson, “A note on Saalfrank's generalization of absolute retract,” Proc. Am. Math. Soc.,15, No. 2, 308–310 (1964).
H. Rostaniec, “On the likeness of nontrivial AR-spaces to the Hilbert cube,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 9, 879–883 (1977).
C. W. Saalfrank, “Neighborhood retraction generalized for compact Hausdorff spaces,” Portug. Math.,20, No. 1–2, 11–16 (1961).
C. W. Saalfrank, “A generalization of the concept of absolute retract,” Proc. Am. Math. Soc.,12, No. 3, 374–378 (1961).
C. W. Saalfrank, “A characterization of contractible compact Hausdorff spaces,” Portug. Math.,21, No. 1–2, 59–60 (1962).
Katsuro Sakai, “On embeddings of infinite-dimensional manifold pairs,” Sci. Repts. Tokyo Kyoiku Daigaku,12, No. 329–346, 202–213 (1974).
Katsuro Sakai, “Embeddings of infinite-dimensional manifold pairs and remarks on stability and deficiency,” J. Math. Soc. Jpn.,29, No. 2, 261–280 (1977).
Katsuro Sakai, “Replacing maps by embeddings between [0, 0)-stable Q-manifolds pairs,” Math. Jpn.,22, No. 1, 93–98 (1977).
Katsuro Sakai, “Some properties of MAR and MANR,” Tohoku Math. J.,30, No. 3, 351–366 (1978).
S. Sakai, “On extensions of mappings into n-cubes,” Proc. Jpn. Acad.,44, No. 9, 939–943 (1968).
D. E. Sanderson, “An infinite-diemnsional Schoenflies theorem,” Trans. Am. Math. Soc.,148, No. 1, 33–39 (1970).
R. M. Schori and J. E. West, “The hyperspace of the closed unit interval is a Hilbert cube,” Trans. Am. Math. Soc.,213, 217–235 (1975).
L. I. Sennott, “On extending continuous functions into a metrizable A. E.,” Gen. Topol. Appl.,8, No. 3, 219–228 (1978).
J. P. Serre, “Extension des applications-homotopie,” Sém. H. Cartan. École Norm Supér., 1949–1950,2, No. 1, 1–6 (1956).
R. B. Sher, “Products and sums of absolute proper retracts,” Colloq. Math.,33, No. 1, 91–102 (1975).
R. B. Sher, “A theory of absolute proper retracts,” Fundam. Math.,88, No. 3, 241–247 (1975).
R. B. Sher, “Docility at infinity and compactifications of ANRs,” Trans. Am. Math. Soc.,221, No. 1, 213–224 (1976).
R. B. Sher, “The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube,” Proc. Am. Math. Soc.,63, No. 1, 150–152 (1977).
R. B. Sher, “Products and sums of absolute proper retracts. II,” Colloq. Math.,40, No. 2, 223–225 (1979).
K. Sieklucki, “A generalization of a theorem of K. Borsuk concerning the dimension of ANR-sets,” Bull. Acad. Pol. Sci. Sér. Sci., Math., Astron. Phys.,10, No. 8, 433–436 (1962).
K. Sieklucki, “Shift-invariant subsets of the Hilbert cube,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,23, No. 12, 1265–1272 (1976).
R. Sikorski, “On the operation of cutting off mappings,” Prace Mat.,1, 136–140 (1955).
S. Singh, “N-adic decompositions and retracts,” Stud. Topol., New York, 545–551 (1975).
S. Singh, “On a question of Borsuk on FARs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,23, 267–269 (1975).
S. Singh, “A three-dimensional absolute retract,” Lect. Notes Math.,378, 443–448 (1974).
S. Singh, “Three-dimensional ARs which do not contain two-dimensional ANRs,” Fundam. Math.,93, No. 1, 23–36 (1976).
S. Singh, “A linking axiom and retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,26, No. 9–10, 817–823 (1978).
S. Singh, “On a problem of Borsuk,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,27, No. 1, 129–134 (1979).
S. Singh, “An R-stable ANR which is not FR-stable,” Fundam. Math.,103, No. 3, 177–182 (1979).
S. Singh, “Toroidal decompositions of S3 and a family of three-dimensional ANRs (ARs),” Fundam. Math.,112, No. 1, 69–79 (1981).
E. H. Spanier and J. H. C. Whitehead, “Obstructions to compression,” Quart. J. Math.,6, No. 22, 91–100 (1955).
T. E. Stewart, “On R-equivalent spaces,” Proc. Koninkl. Nederl. Akad. Wet.,A61, No. 4, 460–462 (1958).
M. Strok, “A remark on Borsuk's paper ‘On fundamental deformation retracts and on some related notions,’” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,23, No. 7, 767–769 (1975).
W. L. Strother, “Multihomotopy,” Duke Math J.,22, No. 2, 281–285 (1955).
W. L. Strother, “Fixed points, fixed sets and M-retracts,” Duke Math. J.,22 No. 4, 551–556 (1955).
W. L. Strother and L. E. Ward, Jr., “Retracts from neighborhood retracts,” Duke Math. J.,25, No. 1, 11–14 (1958).
A. Suszycki, “On extensions of multivalued maps,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,27, No. 2, 183–188 (1979).
A. C. Thompson, “Isometric embedding in Hilbert space,” Nieuw Arch. Wisk.,25, No. 2, 161–168 (1977).
A. Tominaga, “On extensions of a metric,” J. Sci. Hiroshima Univ.,A17, No. 2, 185–191 (1953).
H. Toruńczyk, “On factors of the Hilbert cube and metric properties of retractions,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,24, No. 9, 757–765 (1976).
H. Toruńczyk, “Homeomorphism groups of compact Hilbert cube manifolds which are manifolds,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 4, 401–408 (1977).
H. Toruńczyk, “Concerning locally homotypy negligible sets and characterization ofl 2-manifolds,” Fundam. Math.,101, No. 2, 93–110 (1978).
H. Toruńczyk, “Characteryzacje rozmaitosci neiskończenie Nymairowych,” Rocz. Pol. Tow. Mat., Ser. 2,22, No. 1, 39–43 (1979).
H. Toruńczyk, “On CE-images of the Hilbert cube and characterization of Q-manifolds,” Fundam. Math.,106, No. 1m 39040 (1980).
H. Toruńczyk, “Characterizing Hilbert space topology,” Fundam. Math.,111, No. 3, 247–262 (1981).
K. Tsuda, “On AWNR-spaces in shape theory,” Math. Jpn.,22, No. 4, 471–478 (1977).
E. Tutaj, “A generalization of the second theorem of O. Hanner,” Zesz. Nauk. Univ. Jagiell., No. 203, 109–112 (1969).
E. Tutaj, “Note on a problem of K. Borsuk,” Zesz. Nauk. Univ. Jagiell., No. 203, 113–115 (1969).
C. S. Vora, “Symmetric G-products of A-ANR,” Boll. Unione Math. Ital.,10, No. 1, 6–13 (1974).
C. S. Vora, “Fixed points of certain symmetric product mappings of a compact A-ANR,” Math. Stud., 1974,42, No. 1–4, 379–396 (1975).
An. Vučemilović, “Apsolutni okolinski homotopski retrakti i apsolutni homotopski retrakti za klasu metričkih prostora,” Zb. Trud. Mat. Sojuz Drusht, Mat. Fiz. i Astron. Jugosl.,1, 31–34 (1973).
M. Wada, “Local connectivity of mapping spaces,” Duke Math. J.,22, No. 3, 419–425 (1955).
L. E. Ward, Jr., “Extending Whitney maps,” Pac. J. Math.,93, No. 2, 465–469 (1981).
C. Weber, “Quelques théoremes bein connus sur les A. N. R. et les CW-complexes,” Enseign. Math.,13, No. 3, 211–222 (1967) (1968).
C. Weber, “Deux remarques sur les plongement d'un AR dans un espace euclidien,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,16, No. 11, 851–855 (1968).
J. E. West, “The diffeomorphic excision of closed local compacta from infinite-dimensional Hilbert manifolds,” Compos. Math.,21, No. 3, 271–291 (1969).
J. E. West, “Infinite products which are Hilbert cubes,” Trans. Am. Math. Soc.,150, No. 1, 1–25 (1970).
J. E. West, “Compact ANRs have finite type,” Bull. Am. Math. Soc.,81, No. 1, 163–165 (1975).
J. E. West, “Mapping cylinder of Hilbert cube factors. II. The relative case,” Gen. Topol. Appl.,5, No. 1, 35–44 (1975).
J. E. West, “Mapping Hilbert cube manifolds to ANRs: a solution of a conjecture of Borsuk,” Ann. Math.,106, No. 1, 1–18 (1977).
P. A. White, “Regular convergence,” Bull. Am. Math. Soc.,60, No. 5, 431–443 (1954).
G. T. Whyburn, “Retracting multifunctions,” Proc. Nat. Acad. Sci. U.S.A.,59, No. 2, 343–348 (1968).
R. L. Wilder, “Concerning a problem of Alexandroff,” Michigan Math. J.,3, No. 2, 181–185 (1955–1956).
R. J. Wille, “Sur les espaces faiblement rétractiles,” Proc. Koninkl. Nederl. Akad. Wetensch.,A57, No. 5, 527–532 (1954).
D. C. Wilson, “Mappings with 1-dimensional absolute neighborhood retract fibers,” Gen. Topol. Mod. Anal. Proc. Conf., Riverside, Calif., May 28–31, 1980, New York (1981), pp. 341–343.
R. Y. T. Wong, “On homeomorphism of infinite-diemnsional bundles,” Trans. Am. Math. Soc.,191, 245–259 (1974).
R. Y. T. Wong, “Periodic actions on the Hilbert cube,” Fundam. Math.,85, No. 3, 203–210 (1974).
R. Y. T. Wong and N. Kronenberg, “Unions of Hilbert cubes,” Trans. Am. Math. Soc.,211, 289–297 (1975).
D. G. Wright, “ARs which contain only trivial ANRs,” Houston J. Math.,4, No. 1, 121–127 (1978).
A. L. Yandl, “On δ-continuity, proximate retracts, fixed-points and homotopy,” Doct. Diss. Univ. Wash., 1965, p. 113. Dissert. Abstrs.,26, No. 8, 4704–4705 (1966).
Supplement to the literature
S. M. Ageev, “On properties of contractibility and local contractibility of infinitedimensional spaces,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 4, 29–33 (1980).
S. A. Antonyan, “Spaces of mappings — equivalent absolute extensors,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 6, 22–25 (1981).
V. Bartik, “Aleksandrov-Čech cohomologies and mappings into Eilenberg-MacLane polyhedra,” Mat. Sb.,76, No. 2, 231–238 (1968).
V. N. Basmanov, “Covariant functors, retracts, and dimension,” Dokl. Akad. Nauk SSSR,271, No. 5, 1033–1036 (1983).
V. N. Basmanov, “Covariant functors of finite powers and connectedness,” Dokl. Akad. Nauk SSSR,279, No. 6, 1289–1293 (1984).
V. N. Basmanov and A. G. Savchenko, “The space of retractions of the segment is homeomorphic to Hilbert space,” in: V Tiraspol' Symp. Gen. Topol. Appl., Shtiintsa, Kishinev (1985), pp. 20–21.
S. A. Bogatyi, “On metric retracts,” Dokl. Akad. Nauk SSSR,204, No. 3, 522–524 (1972).
S. A. Bogatyi, “On the Vietoris theorem for shapes, inverse limits, and a problem of Yu. M. Smirnov,” Dokl. Akad. Nauk SSSR,211, No. 4, 764–767 (1973).
S. A. Bogatyi, “Approximation and fundamental retracts,” Mat. Sb.,93, No. 1, 90–102 (1974).
S. A. Bogatyi, “On the Vietoris theorem in the category of homotopies and a problem of Borsuk,” Fundam. Math.,84, No. 3, 209–228 (1974).
S. A. Bogatyi, “The number of periodic points of a mapping of the segment grows exponentially,” Soobshch. Akad. Nauk GrSSR,212, No. 1, 25–28 (1986).
S. A. Bogatyi and Yu. M. Smirnov, “On the position of compacta in Hilbert space,” Czech. Math. J.,26, No. 1, 37–42 (1976).
K. Borsuk, Theory of Retracts [Russian translation], Mir, Moscow (1971).
K. Borsuk, Shape Theory [Russian translation], Mir, Moscow (1976).
V. I. Golov, “Ordered arcs of Peano continua. Fiber version,” Vestn. Mosk. Gos. Univ., Ser. Mat., No. 3, 77–79 (1984).
V. I. Golov, “Hilbert space as a hyperspace of ordered arcs,” Funkts. Anal. Prikl. Mekh. Teorii Veroyatn., 13–18 (1984).
A. N. Dranishnikov, “Absolute extensors in dimension n and n-soft mappings which raise dimension,” Usp. Mat. Nauk,39, No. 5, 55–95 (1984).
A. N. Dranishnikov, “Multivalued absolute retracts and absolute extensors in dimension 0 and 1,” Usp. Mat. Nauk,39, No. 5, 241–242 (1984).
Zh. Zhivanovich, “Union and product of w-spaces,” Mat. Vesn.,5, No. 2, 235–238 (1981).
A. V. Zarelua, “On continuation of mappings to extensions possessing certain special properties,” Sib. Mat. Zh.,5, No. 3, 532–548 (1964).
M. M. Zarichnyi, “Free topological groups of absolute neighborhood retracts and infinite-dimensional manifolds,” Dokl. Akad. Nauk SSSR,266, No. 3, 541–544 (1982).
M. M. Zarichnyi, “On subfunctors of the superextension functor,” Preprint, Moscow State Univ. (1982).
M. M. Zarichnyi, “Symmetric products which are infinite-dimensional manifolds,” Vestn. L'vov. Univ. Ser. Mekh.-Mat., 65–69 (1985).
A. V. Ivanov, “Superextensions of metrizable continua and of the generalized Cantor discontinuum,” Dokl. Akad. Nauk SSSR,254, No. 2, 279–281 (1980).
S. S. Kotanov, “The Kuratowski-Dugundji theorem in shape theory,” Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 6, 33–39 (1980).
S. S. Kotanov, “Extension of fundamental mappings,” Sib. Mat. Zh.,24, No. 3, 92–101 (1983).
V. I. Kuz'minov, “Homological theory of dimension,” Usp. Mat. Nauk,23, No. 5, 3–49 (1968).
B. T. Levshenko, “The dimension of metric spaces and retraction,” Fundam. Math.,66, No. 1, 1–5 (1969).
B. T. Levshenko and Yu. M. Smirnov, “On a property of zero-dimensional metric spaces,” Gen. Topol. Relat. Mod. Anal. Alegebra, Vol. 2, Prague (1967), pp. 241–242.
Yu. T. Lisitsa, “On obstructions to the extension of mappings,” Sib. Mat. Zh.,20, No. 2, 337–344 (1979).
M. Madirimov, “On extension of equivariant mappings,” Mat. Sb.,98, No. 1, 84–92 (1975).
V. I. Malykhin and V. I. Ponomarev, “General topology (set-theoretic direction),” J. Sov. Math.,7, No. 4 (1977).
L. E. Mednikov, “Homeomorphisms of Z-sets into Iℵ1,” Topol. Teoriya Mnozhestv. Izhevsk (1982), pp. 53–55.
G. M. Nepomnyashchii, “On selection and extension of uniformly continuous mappings,” Dokl. Akad. Nauk SSSR,240, No. 6, 1289–1292 (1978).
G. M. Nepomnyashchii, “On the structure of multivalued absolute retracts,” Tr. Mosk. Mat. Obshch.,47, 146–157 (1984).
V. V. Obukhovskii and A. G. Skaletskii, “Some theorems on extension and quasiextension of continuous mappings,” Sib. Mat. Zh.,23, No. 4, 137–141 (1982).
N. G. Okormeshko, “On retractions of homogeneous spaces,” Dokl. Akad. Nauk SSSR,268, No. 3, 548–551 (1983).
B. A. Pasynkov, V. V. Fedorchuk, and V. V. Filippov, “Dimension theory,” J. Sov. Math.,18, No. 5 (1982).
A. G. Savchenko, “On properties of the mapping expn c f,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., No. 1, 19–25 (1985).
A. G. Savchenko, “The functor expn c, absolute retracts, and Hilbert space,” Mat. Zametki,38, No. 6, 875–887 (1985).
Yu. M. Smirnov, “On equivariant imbeddings of G-spaces,” Usp. Mat. Nauk,31, No. 5, 137–147 (1976).
Yu. M. Smirnov, “Shape theory. I,” J. Sov. Math.,23, No. 6 (1983).
M. V. Smurov, “On homeomorphisms of spaces of probability measures of uncountable powers of compacta,” Usp. Mat. Nauk,38, No. 3, 187–188 (1983).
V. V. Fedorchuk, “On the dimension of x-metrizable bicompacta, in particular, Dugundji spaces,” Dokl. Akad. Nauk SSSR,234, No. 1, 30–33 (1977).
V. V. Fedorchuk, “On some geometric properties of covariant functors,” Usp. Mat. Nauk,39, No. 5, 169–208 (1984).
Ya. N. Khaimov, “The homotopy type of a space having a briquet decomposition,” Dokl. Akad. Nauk TadzhSSR,22, No. 1, 25–29 (1979).
T. Chapman, Lectures on Q-Manifolds [Russian translation], Mir, Moscow (1981).
P. V. Chernikov, “Extension of measurable mappings,” Sib. Mat. Zh.,22, No. 2, 227–229 (1981).
A. Ch. Chigogidze, “Uncountable powers of the line, the natural series, and n-soft mappings,” Dokl. Akad. Nauk SSSR,278, No. 1, 50–53 (1984).
A. Ch. Chigogidze, “Nonbicompact absolute extensors in dimension n, n-soft mappings, and their applications, Izv. Akad. Nauk SSSR,50, No. 1, 156–180 (1986).
L. V. Shirokov, “External characterization of Dugundji spaces and kappa-metrizable bicompacta,” Dokl. Akad. Nauk SSSR,263, No. 5, 1073–1077 (1982).
E. V. Shchepin, “Functors and uncountable powers of compacta,” Usp. Mat. Nauk,36, No. 3, 3–62 (1981).
E. V. Shchepin, “The method of inverse spectra in the topology of bicompacta,” Mat. Zametki,31, No. 2, 299–315 (1982).
T. Akasaki, “The Eilenberg-Borsuk duality theorem for metric spaces,” Duke Math. J.,32, No. 4, 653–659 (1965).
R. A. Alo, “Results related to p-embedding,” Topics Topol., Amst.-London, 29–40 (1974).
R. D. Anderson and D. C. Kay, “Commuting maps lacking commuting extensions,” Am. Math. Mon.,74, No. 2, 183–184 (1967).
R. D. Anderson, “On topological infinite deficiency,” Mich. Math. J.,14, No. 3, 365–383 (1967).
R. D. Anderson, “Topological properties of the Hilbert cube and the infinite product of open intervals,” Trans. Am. Math. Soc.,126, No. 2, 200–216 (1967).
R. D. Anderson, “Strongly negligible sets in Fréchet manifolds,” Bull. Am. Math. Soc.,75, No. 1, 64–67 (1969).
R. D. Anderson, “Homeomorphisms of infinite-dimensional manifolds,” Actes Congr. Int. Mathématiciens, Vol. 2, Paris 13–18 (1971).
R. D. Anderson and T. A. Chapman, “Extending homeomorphisms to Hilbert cube manifolds,” Pac. J. Math.,38, No. 2, 281–293 (1971).
R. D. Anderson, D. W. Curtis, and J. van Mill, “A fake topological Hilbert space,” Trans. Am. Math. Soc.,272, No. 1, 311–321 (1982).
R. D. Anderson and R. Shori, “A factor theorem for Fréchet manifolds,” Bull. Am. Math. Soc.,75, No. 1, 53–56 (1969).
J. J. Andrews and M. L. Curtis, “n-space modulo an arc,” Ann. Math.,75, No. 1, 1–7 (1962).
S. Armentrout, “UV properties of compact sets,” Trans. Am. Math. Soc.,143, 487–498 (1969).
S. Armentrout, “Cellular decompositions of 3-manifolds, that yield 3-manifolds,” Mem. Am. Math. Soc., No. 107, 72 (1971).
S. Armentrout and T. Price, “Decompositions into compact sets with UV properties,” Trans. Am. Math. Soc.,141, July, 433–442 (1969).
A. Asada, “Contraction of the group of diffeomorphisms of Rn,” Proc. Jpn. Acad.,41, No. 4, 273–276 (1965).
C. E. Aull, “On C- and C*-embeddings,” Indag. Math.,37, No. 1, 26–33 (1975).
P. Bacon, “Extending a complete metric,” Am. Math. Mon.,75, No. 6, 642–643 (1968).
R. H. Bing, “Retractions onto spheres,” Am. Math. Mon.,71, No. 5, 481–484 (1964).
R. H. Bing and K. Borsuk, “A three-dimensional absolute retract which does not contain any disk,” Fundam. Math.,54, No. 2, 159–175 (1964).
E. Bonan, “Sur un lemme adapté au théoréme de Tietze-Urysohn,” C. R. Acad. Sci.,270, No. 19, A1226–A1228 (1970).
C. J. R. Borges, “On stratifiable spaces,” Pac. J. Math.,17, No 1, 1–16 (1966).
C. J. R. Borges, “Continuous extensions,” Proc. Am. Math. Soc.,18, No. 5, 874–878 (1967).
C. J. R. Borges, “On a question of Wojdyslawski and Strother,” Duke Math. J.,35, No. 4, 829–833 (1968).
C. J. R. Borges, “Connectivity of function spaces,” Can. J. Math.,23, No. 5, 759–763 (1971).
C. J. R. Borges, “Absolute extensor spaces: a correction and an answer,” Pac. J. Math.,50, No. 1, 29–30 (1974).
K. Borsuk, “Bericht über einige neue Ergebnisse und Probleme aus dem Gebiet der anschaulichten Topologie,” Jahresber. Dtsch. Math. Ver.,66, No. 3, 94–106 (1964).
K. Borsuk, “On movable compacts,” Fundam. Math.,66, No. 1, 137–146 (1969).
K. Borsuk, “Theory of shapes,” Monogr. Mat. PAN, 59 (1975).
M. Brown, “Some applications of an approximation theorem for inverse limits,” Proc. Am. Math. Soc.,11, No. 3, 478–483 (1960).
R. Cauty, “Convexité topologique et prolongement des fonctions continues,” Compos. Math.,27, No. 3, 233–271 (1973).
R. Cauty, “Produits symétriques de rétractes absolus de voisinage,” C. R. Acad. Sci.,276, No. 5, 359–361 (1973).
R. Cauty, “Un théoréme de sélection et l'espace des rétractions d'une surface,” Am. J. Math.,97, No. 1, 282–290 (1975).
Z. Cerin, “Hilbert cube modulo an arc,” Fundam. Math.,101, No. 2, 111–119 (1978).
Z. Cerin, “On cellular decompositions of Hilbert cube manifolds,” Pac. J. Math.,91, No. 1, 47–69 (1980).
T. A. Chapman, “On some applications of infinite-dimensional manifolds to the theory of shape,” Fundam. Math.,76, No. 3, 181–193 (1972).
T. A. Chapman, “Shapes of finite-dimensional compacta,” Fundam. Math.,76, No. 3, 261–276 (1972).
T. A. Chapman, “Some results on shapes and fundamental absolute retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,20, No. 1, 37–40 (1972).
T. A. Chapman, “Shapes of some decomposition spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,20, No. 8, 653–656 (1972).
T. A. Chapman, “Characterizing shapes of compacta,” Bull. Am. Math. Soc.,78, No. 5, 847–851 (1972).
T. A. Chapman, “Canonical extensions of homeomorphisms,” Gen. Topol. Appl.,2, No. 3, 227–247 (1972).
T. A. Chapman, “Locally-trivial bundles and microbundles with infinite-dimensional fibers,” Proc. Am. Math. Soc.,37, No. 2, 595–602 (1973).
T. A. Chapman, “Some recent results on compact Hilbert cube manifolds,” Topics Topol., Amst.-London, 139–144 (1974).
M. H. Clapp, “On a generalization of absolute neighborhood retracts,” Fundam. Math.,70, No. 2, 117–130 (1971).
W. W. Comfort, “Retractions and other continuous maps from βX onto βX\X,” Trans. Am. Math. Soc.,114, No. 1, 1–9 (1965).
J. L. Cornette, “Retracts of the pseudoarc,” Colloq. Math.,19, No. 2, 235–239 (1968).
J. L. Cornette and J. E. Cirolo, “Connectivity retracts of finitely coherent Peano continua,” Fundam. Math.,61, No. 2, 177–182 (1967).
D. W. Curtis, “Property Z for function-graphs and finite-dimensional sets in I∞ and S,” Compos. Math.,22, No. 1, 19–22 (1970).
D. W. Curtis, “Some theorems and examples on local equiconnectedness and its specializations,” Fundam. Math.,72, No. 2, 101–113 (1971).
D. W. Curtis, “Simplicial maps which stabilize to near-homeomorphisms,” Compos. Math.,25, No. 2, 117–122 (1972).
D. W. Curtis, “The hyperspace of subcontinua of a Peano continuum,” Lect. Notes Math.,378, 108–118 (1974).
D. W. Curtis, “Growth hyperspaces of Peano continua,” Trans. Am. Math. Soc.,238, 271–238 (1978).
D. W. Curtis and G. Kozlowski, “Brick decompositions and Q-manifolds,” Proc. Am. Math. Soc.,72, No. 1, 170–174 (1978).
D. W. Curtis and R. M. Schori, “Hyperspaces of Peano continua are Hilbert cubes,” Fundam. Math.,101, No. 1, 19–38 (1978).
S. Z. Ditor, “On a lemma of Milutin concerning averaging operators in continuous function spaces,” Trans. Am. Math. Soc.,149, No. 2, 443–452 (1970).
S. Z. Ditor and R. Haydon, “On absolute retracts, P(S), and complemented subspaces of C(Dℵ1),” Stud. Math.,56, No. 3, 243–251 (1976).
T. Dobrowolski, “An extension of a theorem of Klee,” Gen. Topol. Relat. Mod. Anal. Algebra,5, Berlin, 147–150 (1983).
E. K. van Douwen, “Simultaneous linear extension of continuous functions,” Gen. Topol. Appl.,5, No. 4, 297–319 (1983).
A. Dow, “Absolute C-embedding of spaces with countable character and pseudocharacter conditions,” Can. J. Math.,32, No. 4, 945–956 (1980).
J. Dugundji, “An extension of Tietze's theorem,” Pac. J. Math.,1, 353–367 (1951).
E. Dyer, “Regular mappings and dimension,” Ann. Math.,67, No. 1, 119–149 (1958).
E. Dyer and S. Eilenberg, “An adjunction theorem for locally equiconnected spaces,” Pac. J. Math.,41, No. 3, 669–685 (1972).
C. Eberhart, “A unique factorization theorem for countable products of circles,” Fundam. Math.,61, No. 3, 305–308 (1972).
C. Eberhart, “Tychonoff cubes are coset spaces,” Proc. Am. Math. Soc.,19, No. 1, 185–188 (1968).
D. A. Edwards and R. Geoghegan, “Compacta weak shape equivalent to ANRs,” Fundam. Math.,90, No. 2, 115–124 (1976).
R. L. Ellis, “Extending continuous functions of zero-dimensional spaces,” Math. Ann.,186, No. 2, 114–122 (1970).
R. L. Ellis, “Extending uniformly continuous pseudoultrametrics and uniform retracts,” Proc. Am. Math. Soc.,30, 599–602 (1971).
R. Engelking, “On closed images of the space of irrationals,” Proc. Am. Math. Soc.,21, No. 3, 583–586 (1969).
E. Fadell, “Recent results in the fixed point theory of continuous maps,” Bull. Am. Math. Soc.,76, No. 1, 10–29 (1970).
Z. Frolik, J. Pelant, and J. Vilimovsky, “Extensions on uniformly continuous functions,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,26, No. 2, 143–148 (1978).
Z. Furdzik, “On the uniqueness of decomposition into Cartesian product of two curves,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,14, No. 2, 57–61 (1966).
T. E. Gantner, “Extensions of uniform structures,” Fundam. Math.,66, No. 3, 263–281 (1970).
R. Geoghegan, “Manifolds of peicewise linear maps and a related normed linear space,” Bull. Am. Math. Soc.,77, No. 4, 629–632 (1971).
R. Geoghegan, “On spaces of homeomorphisms, embeddings, and functions. II. The piecewise linear case,” Proc. Lon. Math. Soc.,27, Part 3, 463–483 (1973).
R. Geoghegan and R. R. Summerhill, “Infinite-dimensional methods in finite-dimensional geometric topology,” Bull. Am. Math. Soc.,78, No. 6, 1009–10104 (1972).
R. Geoghegan and R. R. Summerhill, “Concerning the shapes of finite-dimensional compacta,” Trans. Am. Math. Soc.,179, May, 281–292 (1973).
R. Geoghegan and R. R. Summerhill, “Finite-dimensional spaces having many of the topological properties of separable Hilbert spacel 2,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,22, No. 9, 949–954 (1974).
Z. Gmurczyk, “Approximative retracts and fundamental retracts,” Colloq. Math.,23, No. 1, 61–63 (1971).
S. Godlewski, “Mutational retracts and extensions of mutations,” Fundam. Math.,84, No. 1, 47–65 (1974).
S. Godlewski, “On the shape of MAR and MANR-spaces,” Fundam. Math.,88, No. 2, 87–94 (1975).
G. R. Gordh, Jr. and L. Lum, “Monotone retracts and some characterizations of dendrites,” Proc. Am. Math. Soc.,59, No. 1, 156–158 (1976).
L. Gorniewicz, “Fixed point theorem for multivalued mappings of approximative ANRs,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,18, No. 8, 431–436 (1970).
T. Goto, “Homotopical cohomology groups of paracompact spaces,” Sci. Rep. Tokyo Kyoiku Daigaku,A9, No. 214–219, 163–169 (1967).
N. R. Gray, “Note on a paper of Wojdyslawski,” Fundam. Math.,63, No. 2, 215–216 (1968).
N. R. Gray, “On the conjecture 2x≈Iω,” Fundam. Math.,66, No. 1, 45–52 (1969).
J. H. Gresham, “A class of infinite-dimensional spaces. Part II: An extension theorem and the theory of retracts,” Fundam. Math.,107, No. 3, 237–245 (1980).
J. de Groot, G. A. Jensen, and A. Verbeek, “Superextensions,” Rept. Math. Cenrum.,ZW, No. 17 (1968).
W. E. Haver, “A characterization theorem for cellular maps,” Bull. Am. Math. Soc.,76, No. 6, 1277–1280 (1970).
W. E. Haver, “Locally contractible spaces that are absolute neighborhood retracts,” Proc. Am. Math. Soc.,40, No. 1, 280–284 (1973).
W. E. Haver, “The closure of the space of homeomorphisms on a manifold,” Trans. Am. Math. Soc.,195, No. 468, 401–409 (1974).
R. Haydon, “On a problem of Pleczyński: Milutin spaces, Dugundji spaces and AE(0-dim),” Stud. Math. (PRL),52, No. 1, 23–31 (1974).
R. W. Heath, “Some comments on simultaneous extensions of mappings on closed subsets,” Lect. Notes Math.,375, 114–119 (1974).
R. W. Heath, “Some remarks on extension theorems in monotonically normal spaces,” Lect. Notes Math.,378, 201–206 (1974).
R. W. Heath and D. J. Lutzer, “Dugundji extension theorems for linearly ordered spaces,” Pac. J. Math.,55, No. 2, 419–425 (1974).
R. W. Heath and D. J. Lutzer, “The Dugundji extension theorem and collectionwise normality, Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,22, No. 8, 827–830 (1974).
R. W. Heath, D. J. Lutzer, and P. L. Zenor, “Monotonically normal spaces,” Trans. Am. Math. Soc.,178, Apr., 481–493 (1973).
R. W. Heath, D. J. Lutzer, and P. L. Zenor, “On continuous extenders,” Stud. Topol., New York, 203–213 (1975).
D. W. Henderson, “Open subsets of Hilbert space,” Compos. Math.,21, No. 3, 312–318 (1969).
C. J. Himmelberg, “Some theorems on equiconnected and locally equiconnected spaces,” Trans. Am. Math. Soc.,115, No. 3, 43–53 (1965).
B. Hoffmann, “A surjective characterization of Dugundji spaces,” Proc. Am. Math. Soc.,76, No. 1, 151–156 (1979).
W. Holsztynski, “On spaces with regular decomposition, “ Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,12, No. 10, 607–611 (1964).
P. J. Huber, “Homotopical cohomology and Čech cohomology,” Math. Ann.,144, No. 1, 73–76 (1961).
D. M. Hyman, “A category larger than the metric and CW-categories,” Mich. Math. J.,15, No. 2, 193–214 (1968).
J. R. Isbell, “Uniform neighborhood retracts,” Pac. J. Math.,11, No. 2, 609–648 (1961).
K. Iseki, “On extension of semifield valued linear functionals,” Proc. Jpn. Acad.,44, No. 8, 796–797 (1968).
W. Jaco and D. R. McMillan, Jr., “Retracting three-manifolds onto finite graphs,” Ill. J. Math.,14, No. 1, 150–158 (1970).
J. W. Jaworowski, “Continuous homology properties of approximative retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,18, No. 7, 359–362 (1970).
J. W. Jaworowski, “Equivariant extensions of maps,” Pac. J. Math.,45, No. 1, 229–244 (1973).
J. W. Jaworowski, “Extending equivariant maps for compact Lie group actions,” Bull. Am. Math. Soc.,79, No. 4, 698–701 (1973).
J. W. Jaworowski, “Equivariant extensions of maps for compact Lie group actions,” Top. Appl. Proc. Conf. Mem. Univ. Newfoundland, St. John's, Canada, 1973, Vol. 12, New York (1975), p. 123.
J. W. Jaworowski, “Extensions of G-maps and Euclidean G-retracts,” Math. Z.,146, No. 2, 143–148 (1976).
J. W. Jaworowski, “An equivariant extension theorem and G-retracts with finite structure,” Manuscr. Math.,35, No. 3, 323–329 (1981).
V. Klee, “Some topological properties of convex sets,” Trans. Am. Math. Soc.,78, No. 1, 30–45 (1955).
J. Klisowski, “A survey of various modifications of absolute retracts and absolute neighborhood retracts,” Colloq. Math.,46, No. 1, 23–35 (1982).
R. J. Knill, “Q-simplicial spaces,” Ill. J. Math.,14, No. 1, 40–51 (1970).
C. W. Kohls and L. G. Lardy, “Extensions and retractions of algebras of continuous functions,” Ill. J. Math.,12, No. 4, 539–549 (1968).
G. Kozlowski, “Factorization of certain maps up to homotopy,” Proc. Am. Math. Soc.,21, No. 1, 89–92 (1969).
B. Krakus and A. Trybulec, “A strongly convex and not contractible metric space,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,15, No. 12, 855–860 (1967).
W. Kuperberg, “On compact metric space sequences, monotonie by r-domination,” Fundam. Math.,60, No. 1, 95–104 (1967).
K. Kuratowski and R. C. Lacher, “A theorem on the space of monotone mappings,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,17, No. 12, 797–800 (1969).
S. Kwasik, “On the equivariant homotopy of G-ANRs,” Proc. Am. Math. Soc.,83, No. 1, 193–194 (1981).
K. W. Kwun, “Upper semicontinuous decompositions of the n-sphere,” Proc. Am. Math. Soc.,13, No. 2, 284–290 (1962).
K. W. Kwun, “Product of Euclidean spaces modulo an arc,” Ann. Math.,79, No. 1, 104–108 (1964).
K. W. Kwun and F. Raymond, “Factors of cubes,” Am. J. Math.,84, No. 3, 433–440 (1962).
R. C. Lacher, “Cell-like spaces,” Proc. Am. Math. Soc.,20, No. 2, 598–602 (1969).
R. C. Lacher, “Cell-like mappings. I,” Pac. J. Math.,30, No. 3, 717–731 (1969).
R. C. Lacher, “Cellularity criteria for maps,” Mich. Math. J.,17, No. 4, 385–396 (1970).
R. C. Lacher, “Cell-like mappings. II,” Pac. J. Math.,35, No. 3, 649–660 (1970).
R. C. Lacher, “Cell-like mappings and their generalizations,” Bull. Am. Math. Soc.,83, No. 4, 495–552 (1977).
R. C. Lacher and D. R. McMillan, Jr., “Partially acyclic mappings between manifolds,” Am. J. Math.,94, No. 1, 246–266 (1972).
P. W. Liebnitz, Jr., Neighborhood Extensions of Continuous Maps, Doct. Diss. Univ. Kansas, 1964. Dissert. Abstrs.,26, No. 1, 390 (1965).
P. E. Long and W. D. Hammers, “Certain noncontinuous retract functions,” Math. Chron.,4, No. 2–3, 122–140 (1976).
D. Lutzer and H. Martin, “A note on the Dugundji extension theorem,” Proc. Am. Math. Soc.,45, No. 1, 137–139 (1974).
D. Lutzer and T. C. Przymusiński, “Continuous extenders in normal and collectionwise normal spaces,” Fundam. Math.,102, No. 3, 165–171 (1979).
J. Luukkainen, “Extension of locally uniformly equivalent metrics,” Colloq. Math.,46, No. 2. 2052–7 (1982).
T. Mackowiak, “Monotone retracts of an arcwise connected continuum,” Colloq. Math.,40, No. 2, 227–233 (1979).
T. Mackowiak, “Retracts of hereditarily unicoherent continua,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,28, No. 3–4, 177–183 (1980).
S. Mardešić, “Retracts in shape theory,” Glas. Mat.,6, No. 1, 153–163 (1971).
S. Mardešić, “Decreasing sequences of cubes and compacta of trivial shape,” Gen. Topol. Appl.,2, No. 1, 17–23 (1972).
S. Mardešić, “Shapes for topological spaces,” Gen. Topol. Appl.,3, No. 3, 265–282 (1973).
S. Mardešić, “A remark on shape deformation retracts,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,25, No. 5, 499–500 (1977).
S. Mardešić and J. Segal, “Shapes of compacta and ANR-systems,” Fundam. Math.,71, No. 1, 41–59 (1971).
V. Mardešić, “On the homogeneity of the Tychonoff cube,” Mat. Vesn.,4, No. 1, 31–32 (1980).
J. R. Martin, “Neighborhood contractible spaces,” Proc. Am. Math. Soc.,87, No. 1, 154–158 (1983).
B. L. McAllister, “Hyperspaces and multifunctions. The first half-century (1900–1950),” Neuw. Arch. Wisk.,26, No. 2, 309–329 (1978).
L. F. McAuley, “Concerning open selections,” Lect. Notes Math., No. 171, 49–53 (1970).
R. A. McCoy, “Some applications of Henderson's open embedding theorem of F-manifolds,” Compos. Math.,21, No. 3, 295–298 (1969).
W. D. McIntosh, “Some theorems in the theory of retracts,” Doct. Diss. Univ. Kans., 1965. Dissert. Abstrs.,26, No. 6, 3374 (1965).
W. D. McIntosh, “Adjunction of locally equiconnected spaces,” Fundam. Math.,63, No. 2, 175–192 (1968).
D. R. McMillan, Jr., “A criterion for cellularity in a manifold,” Ann. Math.,79, No. 2, 327–337 (1964).
D. R. McMillan, Jr., “A criterion for cellularity in a manifold. II,” Trans. Am. Math. Soc.,126, No. 2, 217–224 (1967).
E. Michael, “Convex structures and continuous selections,” Can. J. Math.,11, No. 4, 556–575 (1959).
E. Michael and C. Pixley, “A unified theorem on continuous selections,” Pac. J. Math.,87, No. 1, 187–188 (1980).
J. van Mill and M. van de Vel, “Path connectedness, contractibility and LC-properties of superextensions,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,26, No. 3, 261–269 (1978).
J. van Mill and M. van de Vel, “On superextensions and hyperspaces,” Math. Centre Tracts. Amsterdam, No. 115 (1979), pp. 169–180.
J. van Mill and M. van de Vel, “Subbases, convex sets, and hyperspaces,” Pac. J. Math.,92, No. 2, 385–402 (1981).
J. Milnor, “On spaces having the homotopy type of a CW-complex,” Trans. Am. Math. Soc.,90, No. 2, 272–280 (1959).
T. Miwa, “Retraction and extension of mappings of M1-spaces,” Proc. Jpn. Acad.,A58, No. 6, 253–255 (1982).
T. Miwa, “Adjunction spaces of monotonically normal spaces and spaces dominated by monotonically normal subsets,” Proc. Am. Math. Soc.,87, No. 3, 536–538 (1983).
T. Mizokami, “On the adjunction spaces of free L-spaces and M1-spaces,” Tsukuba J. Math.,6, No. 1, 9–19 (1982).
J. Morgado, “A theorem on extensions of commuting isotone mappings,” Notos Commun. Mat., No. 15 (1967).
M. Moszynska, “On shape and fundamental deformation retracts. I,” Fundam. Math.,75, No. 2, 145–167 (1972).
M. Moszynska, “On shape and fundamental deformation retracts. II,” Fundam. Math.,77, No. 3, 235–240 (1973).
N. Moulis, “Structures de Fredholm sur les variétés hilbertiennes,” Lect. Notes Math.,259 (1972).
S. Mrowka, “Extending of continuous real functions,” Compos. Math.,21, No. 3, 319–327 (1969).
S. Y. Nedev, “A selection theorem,” Dokl. Bolg. Akad. Nauk,35, No. 7, 873–876 (1982).
S. Newman, “One-point compactifications of Q-manifold factors and infinite mapping cylinders,” Stud. Topol., New York (1975), pp. 411–426.
Nguyen To Nhu, “On the extensions of uniformly continuous mappings,” Colloq. Math.,41, No. 2, 243–252 (1979).
Nguyen To Nhu, “Fundamental deformation retracts and weak deformation retracts in the category of metric spaces and uniformly continuous maps,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,27, No. 11–12, 935–940 (1979).
Nguyen To Nhu, “Extending metrics uniformly,” Colloq. Math.,43, No. 1, 91–97 (1980).
Nguyen Van Khue and Nguyen To Nhu, “Two extensors of metrics,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,29, No. 5–6, 285–291 (1981).
Nguyen Van Khue and Nguyen To Nhu, “Lipschitz extensions and Lipschitz retractions in metric spaces,” Colloq. Math.,45, No. 2, 245–250 (1981).
P. Olum, “Invariants for effective homotopy classification and extension of mappings,” Mem. Am. Math. Soc., No. 37 (1961).
R. Ouzilou, “Classification homotopique des fibres banachiques,” C. R. Acad. Sci.,268, No. 21, A1276–A1278 (1969).
F. W. Owens, “Extensions of commuting isotone functions,” Bull. Am. Math. Soc.,72, No. 6, 965–966 (1966).
R. S. Palais, “The classification of G-spaces,” Mem. Am. Math. Soc., Mo. 36 (1960).
R. S. Palais, “Morse theory of Hilbert manifolds,” Topology,2, No. 4, 299–340 (1963).
R. S. Palais, “Homotopy theory of infinite-dimensional manifolds,” Topology,5, No. 1, 1–16 (1966).
T. Parthasarathy, Selection Theorems and Their Applications, Springer, Berlin (1972).
L. Pasicki, “Retracts in metric spaces,” Proc. Am. Math. Soc.,78, No. 4, 595–600 (1980).
H. Patkowska, “On the uniqueness of the decomposition of finite-diemnsional ANRs into Cartesian products of at most 1-dimensional spaces,” Fundam. Math.,58, No. 1, 89–110 (1966).
H. Patkowska, “A homotopy extension theorem for fundamental sequences,” Fundam. Math.,64, No. 1, 89–110 (1966).
A. Pelczýnski, “Linear extensions, linear averagings, and their application to linear topological classification of spaces of continuous functions,” Rozpr. Mat., No. 58 (1968).
C. P. Pixley, “An example concerning continuous selections on infinite-dimensional spaces,” Proc. Am. Math. Soc.,43, No. 1, 237–244 (1974).
T. Porter, “Sur le type d'homotopie couplé,” C. R. Acad. Sci.,276, No. 14, A985–A987 (1973).
M. J. Powers, “Fixed point theorems for noncompact approximative ANRs,” Fundam. Math.,75, No. 1, 61–68 (1972).
T. M. Price, “A necessary condition that a cellular upper semicontinuous decomposition of En yield En,” Trans. Am. Math. Soc.,122, No. 2, 427–435 (1966).
T. Przymusinski, “Collectionwise normality and extensions of continuous functions,” Fundam. Math.,98, No. 1, 75–81 (1978).
T. Przymusinski, “Extending functions from products with a metric factor and absolutes,” Pac. J. Math.,101, No. 2, 463–475 (1981).
T. G. Raghavan and I. L. Reilly, “On protective and injective objects in some topological categories,” Lect. Notes Math., No. 719, 308–315 (1979).
D. Ravditv, “On extensions of homeomorphisms to homeomorphisms,” Pac. J. Math.,37, No. 2, 481–495 (1971).
C. E. Robinson, “A generalization of retracts,” Doct. Diss. Univ. Alabama, 1962. Dissert. Abstrs.,23, No. 10, 3913 (1963).
F. Roush, R. G. Gibson, and K. R. Kellum, “Darboux retracts,” Proc. Am. Math. Soc.,79, No. 3, 491–494 (1980).
K. Sakai, “The space of retractions of a compact Q-manifold is anl 2-manifold,” Proc. Am. Math. Soc.,83, No. 2, 421–424 (1981).
R. M. Schori, “Inverse limits and near-homeomorphism techniques in hyperspace problems,” Lect. Notes Math.,378, 421–428 (1974).
R. M. Schori and J. E. West, “21 is homeomorphic to the Hilbert cube,” Bull. Am. Math. Soc.,78, No. 3, 402–406 (1972).
L. I. Sennott, “Extending complete continuous pseudometrics,” Colloq. Math.,41, No. 2, 237–241 (1979).
H. L. Shapiro, “A note on extending uniformly continuous pseudometrics,” Bull. Soc. Math. Belg.,18, No. 4, 439–441 (1966).
H. L. Shapiro, “Extensions of pseudometrics,” Can. J. Math.,18, No. 5 981–998 (1966).
L. C. Siebenmann, “Approximating cellular maps by homeomorphisms,” Topology,11, No. 3, 271–294 (1972).
K. Sieklucki, “Correction of ‘A generalization of a theorem of K. Borsuk concerning the dimension of ANR-sets,’” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,12, No. 11, 695 (1971).
K. Sieklucki, “Generalized retractions and fixed points,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,19, No. 10, 945–949 (1971).
K. Sieklucki, “A fixed point problem and the Hilbert cube,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,22, No. 4, 421–426 (1974).
S. Smale, “A Vietoris mapping theorem for homotopy,” Proc. Am. Math. Soc.,8, No. 3, 604–610 (1957).
M. Starbird, “Extending maps from products,” Stud. Topol., New York (1975), pp. 559–564.
M. Starbird, “The Borsuk homotopy extension theorem without the binormality condition,” Fundam. Math.,87, No. 3, 207–211 (1975).
N. E. Steenrod, “A convenient category of topological spaces,” Mich. Math. J.,14, No. 2, 133–152 (1967).
H. Steinlein, “On two results of J. Dugundji about extensions of maps and retractions,” Proc. Am. Math. Soc.,77, No. 2, 289–290 (1979).
R. G. Swan, “The homology of cyclic products,” Trans. Am. Math. Soc.,95, No. 1, 27–68 (1960).
A. Szankowski, “On factors of the Hilbert cube,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,17, No. 11, 703–709 (1969).
A. Szankowski, “Protective potencies and multiplicative extension operators,” Fundam. Math.,67, No. 1, 97–113 (1970).
A. Szulkin, “AR-spaces with continuum left and continuum right r-neighbors,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,21, No. 12, 1117–1122 (1973).
A. Szymanski, “On spaces with binary normal subbase,” Colloq. Math.,46, No. 1, 19–21 (1982).
Y. Tanaka, “On closedness of C-and C*-embeddings,” Pac. J. Math.,68, No. 1, 283–292 (1977).
J. L. Taylor, “A counterexample in shape theory,” Bull. Am. Math. Soc.,81, No. 3, Part 1, 629–632 (1975).
H. Toruńczyk, “Remarks on Anderson's paper ‘On topological infinite deficiency,’” Fundam. Math.,66, No. 3, 393–401 (1970).
H. Toruńczyk, “On estimated extensions of homeomorphisms in metric spaces,” Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron. Phys.,18, No. 1, 13–16 (1970).
H. Toruńczyk, “Compact absolute retracts as factors in the Hilbert space,” Fundam. Math.,83, No. 1, 75–84 (1973).
H. Toruńczyk, “Absolute retracts as factors of normed linear spaces,” Fundam. Math.,86, No. 1, 53–67 (1974).
H. Toruńczyk and J. E. West, “A Hilbert space limit for the iterated hyperspace functor,” Proc. Am. Math. Soc.,89, No. 2, 329–335 (1983).
G. S. Ungar, “ANRs and NESs in the category of mappings on metric spaces,” Fundam. Math.,95, No. 2, 111–127 (1977).
L. Ury, “Extending compatible uniformities,” Topology 4th Colloq., Budapest, 1978, Vol. 2, Amsterdam (1980), pp. 1185–1209.
V. Uspenski, “For any X, the product X×Y is homogeneous for some Y,” Proc. Am. Math. Soc.,87, No. 1, 187–188 (1983).
G. Vidossich, “A theorem on uniformly continuous extensions of mappings defined in finite-dimensional spaces,” Isr. J. Math.,7, No. 3, 207–210 (1969).
C. S. Vora, “Symmetric G products of A-ANR,” Publ. Ist. Mat. Univ. Genova, 30 (1972).
J. de Vries, “A note on topological linearization of locally compact transformation groups in Hilbert space,” Math. Syst. Theory,6, No. 1, 49–59 (1972).
N. R. Wagner, “The space of retractions of the 2-sphere and the annulus,” Trans. Am. Math. Soc.,158, No. 2, 319–329 (1971).
N. R. Wagner, “The space of retractions of a 2-manifold,” Proc. Am. Math. Soc.,34, No. 2, 609–614 (1972).
C. T. C. Wall, “Finiteness conditions for CW-complexes,” Ann. Math.,81, No. 1, 56–69 (1965).
C. T. C. Wall, “Finiteness conditions for CW-complexes. II,” Proc. R. Soc.,A295, No. 1441, 129–139 (1966).
J. J. Walsh, “Cell-like maps which do not raise dimension,” Gen. Topol. Mod. Anal. Proc. Conf., Riverside, Calif., May 28–31, 1980, New York (1981), pp. 317–325.
B. R. Wenner, “Extending maps and dimension theory,” Duke Math. J.,37, No. 4, 627–631 (1970).
J. E. West, “Extending certain transformation group actions in separable, infinite-dimensional Fréchet spaces and the Hilbert cube,” Bull. Am. Math. Soc.,74, No. 5, 1015–1019 (1968).
J. E. West, “Factoring the Hilbert cube,” Bull. Am. Math. Soc.,76, No. 1, 116–120 (1970).
J. E. West, “The subcontinua of a dendron form a Hilbert cube factor,” Proc. Am. Math. Soc.,363, No. 2, 603–608 (1972).
J. E. West, “Sums of Hilbert cube factors,” Pac. J. Math.,54, No. 1, 293–303 (1974).
R. Y.-T. Wong, “On homeomorphisms of infinite dimensional product spaces,” Doct. Diss. Louisiana State Univ. and Agric. and Mech. College, 1966. Dissert. Abstrs.,B27, No. 12, 4486–4487 (1967).
R. Y.-T. Wong, “On homeomorphisms of certain infinite dimensional spaces,” Trans. Am. Math. Soc.,128, No. 1, 148–154 (1967).
G. S. Young, “A condition for the absolute homotopy extension property,” Am. Math. Mon.,71, No. 8, 896–897 (1964).
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 24, pp. 195–270, 1986.
Rights and permissions
About this article
Cite this article
Bogatyi, S.A., Fedorchuk, V.V. Theory of retracts and infinite-dimensional manifolds. J Math Sci 44, 372–423 (1989). https://doi.org/10.1007/BF01676870
Issue Date:
DOI: https://doi.org/10.1007/BF01676870