New proofs of Chapman's mapping theorem and West's mapping cylinder theorem

Authors:
A. Fathi, A. Marin and Y. M. Visetti

Journal:
Proc. Amer. Math. Soc. **67** (1977), 327-334

MSC:
Primary 57A20

DOI:
https://doi.org/10.1090/S0002-9939-1977-0461513-7

MathSciNet review:
0461513

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Abstract | References | Similar Articles | Additional Information

Abstract: This note proves two theorems of the theory of *Q*-manifolds; the original proofs are simplified by using Bing shrinking criterion.

**[1]**Z. Cerin,*On cellular approximations of manifolds*, 1974 (preprint).**[2]**T. A. Chapman,*Notes on Hilbert cube manifolds*, Univ. of Kentucky, 1972 (preprint).**[3]**T. A. Chapman,*Cell-like mappings of Hilbert cube manifolds: solution of a handle problem*, General Topol. Appl.**5**(1975), 123–145. MR**0377894****[4]**T. A. Chapman,*Cell-like mappings of Hilbert cube manifolds: applications to simple homotopy theory*, Bull. Amer. Math. Soc.**79**(1973), 1286–1291. MR**0326740**, https://doi.org/10.1090/S0002-9904-1973-13417-2**[5]**R. D. Edwards,*Siebenmann's variation of West's proof of the ANR theorem*(manuscript).**[6]**M. Handel,*The Bing staircase construction for Q-manifolds*, 1975 (preprint).**[7]**William E. Haver,*Mappings between 𝐴𝑁𝑅s that are fine homotopy equivalences*, Pacific J. Math.**58**(1975), no. 2, 457–461. MR**0385865****[8]**Sze-tsen Hu,*Theory of retracts*, Wayne State University Press, Detroit, 1965. MR**0181977****[10]**A. Marin and Y. M. Visetti,*A general proof of Bing’s shrinkability criterion*, Proc. Amer. Math. Soc.**53**(1975), no. 2, 501–507. MR**0388319**, https://doi.org/10.1090/S0002-9939-1975-0388319-X**[11]**H. Torunczyk,*Concerning locally homotopy negligible sets and characterization of*-*manifolds*, Fund. Math. (to appear).**[12]**James E. West,*Mapping cylinders of Hilbert cube factors*, General Topology and Appl.**1**(1971), no. 2, 111–125. MR**0288788****[13]**R. C. Lacher,*Cell-like mappings. I*, Pacific J. Math.**30**(1969), 717–731. MR**0251714****[14]**T. A. Chapman,*Lectures on Hilbert cube manifolds*, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR**0423357**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0461513-7

Keywords:
*Q*-manifolds,
*Z*-sets,
mapping cylinder,
cell-like mappings,
ANR,
Bing shrinking criterion,
near-homeomorphism

Article copyright:
© Copyright 1977
American Mathematical Society