Cell-like maps that are shape equivalences

Author:
Jung-In K. Choi

Journal:
Proc. Amer. Math. Soc. **108** (1990), 1011-1018

MSC:
Primary 54C56; Secondary 54C55, 57N25

MathSciNet review:
1038759

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Abstract: Let be a cell-like map between metric spaces and set . Even if , where each is closed and each is hereditary shape equivalence, may not be a hereditary shape equivalence. Conditions are placed on the 's to assure that is a hereditary shape equivalence. For example, if , where is closed for each is a hereditary shape equivalence, and has arbitrary small neighborhoods whose boundaries miss then is a hereditary shape equivalence. An immediate consequence is that if is a pairwise disjoint null-sequence and each is a hereditary shape equivalence, then is a hereditary shape equivalence. Previously G. Kozlowski showed that if is a pairwise disjoint null-sequence and each is a hereditary shape equivalence, then is a hereditary shape equivalence, which can be obtained as an immediate corollary of one of our results.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1038759-9

Keywords:
Cell-like map,
hereditary shape equivalence,
ANR,
slice-trivial,
nonde-generacy set,
null-sequence

Article copyright:
© Copyright 1990
American Mathematical Society