Abstract
Characterization of paracompact finite C-spaces via continuous selections avoiding Z σ-sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite C-spaces are also proved.
Similar content being viewed by others
References
Ancel, F.: Proper hereditary shape equivalences preserve property C, Topology Appl. 19 (1985), 71-74.
Addis, D. and Gresham, J.: A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandroff's problem, Fund. Math. 101 (1978), 195-205.
Alexandroff, P.: Zum allgemeinen Dimensionproblem, Nachr. Ges. Göttingen (1928), 25-44.
Alexandroff, P. and Pasynkov, B.: Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian).
Banakh, T. and Trushchak, K.: Z n-sets and the disjoint n-cells property in products of ANR's, Preprint.
Borst, P.: Some remarks concerning C-spaces, Preprint.
Chatyrko, V.: On factorization theorem for transfinite dimension dimC, Preprint.
Dieudonne, J.: Une généralisation des espaces compacts, J. Math. Pures Appl. 23 (1944), 65-76.
Dranishnikov, A., Repovš, D. and Ščepin, E.: Transversal intersection formula for compacta, Topology Appl. 85 (1998), 93-117.
Dowker, C. H.: On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224.
Engelking, R.: Theory of Dimensions: Finite and Infinite, Heldermann-Verlag, Lemgo, 1995.
Engelking, R.: General Topology, 2nd edn, Heldermann, Berlin, 1989.
Gutev, V. and Valov, V.: Continuous selections and C-spaces, Proc. Amer. Math. Soc., to appear.
Hattori, Y. and Yamada, K.: Closed pre-images of C-spaces, Math. Japan. 34(4) (1989), 555-561.
Haver, W.: A Covering Property for Metric Spaces, Lecture Notes in Math. 375, Springer-Verlag, New York, 1974.
Katětov, M.: On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91.
Levin, M., Rubin, L. and Schapiro, P.: The Mardešić actorization theorem for extension theory and C-separation, Preprint.
Michael, E.: Continuous selecions I, Ann. of Math. 63 (1956), 361-382.
Michael, E.: Continuous selections avoiding a set, Topology Appl. 28 (1988), 195-213.
Pasynkov, B.: A factorization of maps onto metric spaces, Dokl. Akad. Nauk SSSR 182 (1968), 268-271 (in Russian).
Pasynkov, B.: A private letter, August 1999.
Pol, E.: The Baire-category method in some compact extension problems, Pacific J. Math. 122 (1986), 197-210.
Pol, R.: A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), 634-636.
Ščepin, E. and Brodskii, N.: Selections of filtered multivalued mappings, Trudy Mat. Inst. Steklova 212 (1996), 220-249 (in Russian).
Skljarenko, E.: A theorem of dimension-lowering mappings, Bull. Acad. Pol. Sci. Ser. Math. 10 (1962), 429-432.
Uspenskij, V.: A selection theorem for C-spaces, Topology Appl. 85 (1998), 351-374.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Valov, V. Continuous Selections and Finite C-Spaces. Set-Valued Analysis 10, 37–51 (2002). https://doi.org/10.1023/A:1014457120871
Issue Date:
DOI: https://doi.org/10.1023/A:1014457120871