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

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

MathSciNet review:
0388319

Full-text PDF

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*-*sphere and the sum of two solid horned spheres*, Ann. of Math. (2)**56**(1952), 354-362. MR**14**, 192. MR**0049549 (14:192d)****[2]**-,*A decomposition of**into points and tame arcs such that the decomposition space is topologically different from*, Ann. of Math. (2)**65**(1957), 484-500. MR**19**, 1187. MR**0092961 (19:1187g)****[3]**-,*The cartesian product of a certain non-manifold and a line is*, Bull. Amer. Math. Soc.**64**(1958), 82-84. MR**20**#3514. MR**0097034 (20:3514)****[4]**J. Dugundji,*Topology*, Allyn and Bacon, Boston, Mass., 1966. MR**33**#1824. MR**0193606 (33:1824)****[5]**R. D. Edwards and L. C. Glaser,*A method for shrinking decomposition of certain manifolds*, Trans. Amer. Math. Soc.**165**(1972), 45-56. MR**45**#4423. MR**0295357 (45:4423)****[6]**L. F. McAuley,*Some upper semi-continuous decompositions of**into*, Ann. of Math. (2)**73**(1961), 437-457. MR**23**#A3554. MR**0126258 (23:A3554)****[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]**K. Morita and S. Hanai,*Closed mappings and metric spaces*, Proc. Japan Acad.**32**(1956), 10-14. MR**19**, 299. MR**0087077 (19:299a)****[9]**A. H. Stone,*Metrizability of decomposition spaces*, Proc. Amer. Math. Soc.**7**(1956), 690-700. MR**19**, 299. MR**0087078 (19:299b)****[10]**I. A. Vainštein,*On closed mappings of metric spaces*, Dokl. Akad. Nauk SSSR**57**(1947), 319-321. (Russian) MR**9**, 153. MR**0022067 (9:153b)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54B15,
57A10

Retrieve articles in all journals with MSC: 54B15, 57A10

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