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]**-,*Cell like mappings of Hilbert cube manifolds*:*solution of a handle problem*, Gen. Topology and Appl.**5**(1975), 123-145. MR**0377894 (51:14063)****[4]**-,*Cell like mappings of Hilbert cube manifolds*:*applications to simple homotopy theory*, Bull. Amer. Math. Soc.**79**(1973), 1286-1291. MR**0326740 (48:5083)****[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]**W. Haver,*Cell like mappings between ANR's are fine homotopy equivalences*, Pacific J. Math.**58**(1975), 457-461. MR**0385865 (52:6724)****[8]**S. T. Hu,*Theory of retracts*, Wayne State Univ. Press, Detroit, Mich., 1965. MR**0181977 (31:6202)****[10]**A. Marin and Y. M. Visetti,*A general proof of Bing shrinkability criterion*, Proc. Amer. Math. Soc.**53**(1975), 501. MR**0388319 (52:9156)****[11]**H. Torunczyk,*Concerning locally homotopy negligible sets and characterization of*-*manifolds*, Fund. Math. (to appear).**[12]**J. E. West,*Mapping cylinder of Hilbert cube factors*, General Topology and Appl.**1**(1971), 111-125. MR**0288788 (44:5984)****[13]**R. C. Lacher,*Cell-like mappings*. I, Pacific J. Math.**30**(1969), 717-731. MR**0251714 (40:4941)****[14]**T. A. Chapman,*Lectures on Hilbert cube manifolds*, delivered at Guilford College, (October 1975), 1976 (preprint). MR**0423357 (54:11336)**

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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