Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Steve Armentrout, Monotone decompositions of E 3, Topology Seminar (Wisconsin, 1965), Ann. of Math. Studies, no. 60, Princeton Univ. Press, Princeton, N. J., 1966, 1–25.
________, UV properties of compact sets, Trans. Amer. Math. Soc. 143 (1969), 487–498.
________, Homotopy properties of decomposition spaces, Trans. Amer. Math. Soc. 143 (1969), 499–507.
________, A decomposition of E 3 into straight arcs and singletons, Dissertationes Math. 73 (1970), 5–46.
________, A three-dimensional speroidal space which is not a sphere, Fund. Math. 68 (1970), 183–186.
________, Cellular decompositions of 3-manifolds that yield 3-manifolds, Memoir 107, Amer. Math. Soc., 1971.
Steve Armentrout and Thomas M. Price, Decompositions into compact sets with UV properties, Trans. Amer. Math. Soc. 141 (1969), 433–442.
B. J. Ball and R. B. Sher, Extending cell-like maps on manifolds.
R. H. Bing, A homeomorphism between the 3-sphere and the sum of two solid horned spheres, Ann. of Math. 56 (1952), 354–362.
_____, A decomposition of E 3 into points and tame arcs such that the decomposition space is topologically different from E 3, Ann. of Math. 65 (1957), 484–500.
_____, Upper semicontinuous decompositions of E 3, Ann. of Math. 65 (1957), 363–374.
_____, The Cartesian product of a certain non-manifold and a line is E 4, Ann. of Math. 70 (1959), 399–412.
_____, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305.
_____, Pointlike decompositions of E 3, Fund. Math. 50 (1962), 431–453.
_____, Radial engulfing, in Conference on the Topology of Manifolds, 1967 (John G. Hocking, ed.), 1–18, Prindle, Weber & Schmidt, Boston, 1968.
_____, these proceedings.
K. Borsuk, Theory of retracts, Monog. Mat., Vol. 44, Polish Scientific Publishers, Warsaw, 1967.
J. L. Bryant and C. L. Seebeck, III, Locally nice embeddings of polyhedra, Quart. J. Math. (Oxford) (2) 21 (1970), 265–272.
C. E. Burgess and J. W. Cannon, Embeddings of surfaces in E 3, Rocky Mountain J. Math. 1 (1971), 259–344.
J. W. Cannon, Sets which can be missed by side approximations to spheres, Pacific J. Math. 34 (1970), 321–334.
________, ULC properties in neighborhoods of embedded surfaces and curves in E 3, Can. J. Math. 25 (1973), 31–73.
________, New proofs of Bing’s approximation theorems for surfaces, Pacific J. Math. 46 (1973), 361–379.
________, Taming cellular decompositions of manifolds, (preprint).
L. O. Cannon, Sums of solid horned spheres, Trans. Amer. Math. Soc. 122 (1966), 203–228.
A. V. Cernavskii, The equivalence of local flatness and local one-connectedness for embeddings of (N−1)-dimensional manifolds in N-dimensional manifolds for N>4.
F. D. Crary, Some new engulfing theorems, Thesis, Univ. of Wisconsin-Madison, 1973.
R. J. Daverman, A new proof for the Hosay-Lininger theorem about crumpled cubes, Proc. Amer. Math. Soc. 23 (1969), 52–54.
________, Locally nice codimension one manifolds are locally flat, Bull. Amer. Math. Soc. 79 (1973), 410–413.
Albrecht Dold, Lectures on Algebraic Topology, Springer Verlag, New York, 1972.
J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
W. T. Eaton, Sewings of crumpled cubes that yield the three sphere, preprint (incorporated into [31]).
_____, Sums of solid spheres, Mich. Math. J. 19 (1972), 193–207.
_____, Applications of a mismatch theorem to decomposition spaces, Fund. Math. (to appear).
_____, A generalization of the Dog Bone Space to E n, Proc. Amer. Math. Soc. 39 (1973), 379–387.
_____, A two-sided approximation theorem for 2-spheres, Pacific J. Math. 44 (1973), 461–485.
W. T. Eaton and C. P. Pixley, these proceedings.
R. D. Edwards, Approximating codimension ≥3 — compacta with locally homotopically unknotted embeddings, preprint, 1974.
R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings, Ann. of Math (2) 93 (1971), 63–88.
R. D. Edwards and R. T. Miller, Cell-like closed 0-dimensional decompositions of R 3 are R 4 factors, preprint, 1974.
M. K. Fort, Jr., A note concerning a decomposition space defined by Bing, Ann. of Math. 65 (1957), 501–504.
Norman Hosay, The sum of a real cube and a crumpled cube is S 3, Notices Amer. Math. Soc. 10 (1963), 666.
R. C. Lacher, Cell-like mappings of ANR’s, Bull. Amer. Math. Soc. 74 (1968), 933–935.
_____, Cell-like mappings I, Pacific J. Math. 30 (1969), 717–731, and II, Pacific J. Math. 35 (1970), 649–660.
L. L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534–549.
L. F. McAuley, Upper semicontinuous decompositions of E 3 into E 3 and generalizations to metric spaces, Topology of 3-manifolds and related topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, 21–26.
_____, Some upper semi-continuous decompositions of E 3 into E 3, Ann. of Math. 73 (1961), 437–457.
D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327–337.
________, Some topological properties of piercing points, Pacific J. Math., 22 (1967), 313–322.
________, Acyclicity in 3-manifolds, Bull. Amer. Math. Soc. 76 (1970), 942–964.
A. Marin and Y. M. Visetti, A general proof of Bing’s shrinkability criterion, preprint, Orsay, 1973.
R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), 416–428.
T. M. Price, A necessary condition that a cellular upper semicontinuous decomposition of E n yield E n, Trans. Amer. Math. Soc. 122 (1966), 427–435.
_____, Decompositions of S 3 and pseudo-isotopies, Trans. Amer. Math. Soc. 140 (1969), 295–299.
T. M. Price and C. L. Seebeck, III, Approximations of somewhere nice codimension one manifolds having 1-ULC complements, I and II.
J. H. Roberts and N. E. Steenrod, Monotone transformations of two-dimensional manifolds, Ann. of Math. 39 (1938), 851–862.
C. L. Seebeck, III, Collaring an (n−1)-manifold in an n-manifold, Trans. Amer. Math. Soc. 148 (1970), 63–68.
R. B. Sher, Realizing cell-like maps in Euclidean space.
L. C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972), 271–294.
E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
M. A. Stan’ko, Approximation of embeddings of compacta in codimensions greater than two, Dokl. Akad. Nauk 12 (1971), 906–909.
W. L. Voxman, On the shrinkability of decompositions of 3-manifolds, Trans. Amer. Math. Soc. 150 (1970), 27–39.
_____, Decompositions of 3-manifolds and pseudo-isotopies, Trans. Amer. Math. Soc. 164 (1972), 503–508.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this paper
Cite this paper
Cannon, J.W. (1975). Taming cell-like embedding relations. In: Glaser, L.C., Rushing, T.B. (eds) Geometric Topology. Lecture Notes in Mathematics, vol 438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066108
Download citation
DOI: https://doi.org/10.1007/BFb0066108
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07137-2
Online ISBN: 978-3-540-37412-1
eBook Packages: Springer Book Archive