A general proof of Bing's shrinkability criterion

Authors:
A. Marin and Y. M. Visetti

Journal:
Proc. Amer. Math. Soc. **53** (1975), 501-507

MSC:
Primary 54B15; Secondary 57A10

MathSciNet review:
0388319

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives a proof of the general Bing shrinkability criterion, including a proof of the fundamental theorem that a shrinkable compact upper semicontinuous decomposition of a complete metric space is realized by a pseudo-isotopy of the space.

**[1]**R. H. Bing,*A homeomorphism between the 3-sphere and the sum of two solid horned spheres*, Ann. of Math. (2)**56**(1952), 354–362. MR**0049549****[2]**R. H. Bing,*A decomposition of 𝐸³ into points and tame arcs such that the decomposition space is topologically different from 𝐸³*, Ann. of Math. (2)**65**(1957), 484–500. MR**0092961****[3]**R. H. Bing,*The cartesian product of a certain non-manifold and a line is 𝐸₄*, Bull. Amer. Math. Soc.**64**(1958), 82–84. MR**0097034**, 10.1090/S0002-9904-1958-10160-3**[4]**James Dugundji,*Topology*, Allyn and Bacon, Inc., Boston, Mass., 1966. MR**0193606****[5]**Robert D. Edwards and Leslie C. Glaser,*A method for shrinking decompositions of certain manifolds*, Trans. Amer. Math. Soc.**165**(1972), 45–56. MR**0295357**, 10.1090/S0002-9947-1972-0295357-6**[6]**Louis F. McAuley,*Some upper semi-continuous decompositions of 𝐸³ into 𝐸³*, Ann. of Math. (2)**73**(1961), 437–457. MR**0126258****[7]**-,*Upper semicontinuous decompositions of**into**and generalizations to metric spaces*, Topology of -Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 21-26. MR**25**#4502.**[8]**Kiiti Morita and Sitiro Hanai,*Closed mappings and metric spaces*, Proc. Japan Acad.**32**(1956), 10–14. MR**0087077****[9]**A. H. Stone,*Metrizability of decomposition spaces*, Proc. Amer. Math. Soc.**7**(1956), 690–700. MR**0087078**, 10.1090/S0002-9939-1956-0087078-6**[10]**I. A. Vaiĭnšteĭn,*On closed mappings of metric spaces*, Doklady Akad. Nauk SSSR (N.S.)**57**(1947), 319–321 (Russian). MR**0022067**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0388319-X

Keywords:
Upper semicontinuous decomposition,
shrinkable,
pseudo-isotopy

Article copyright:
© Copyright 1975
American Mathematical Society