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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A remark on refinable maps and calmness


Author: Hisao Kato
Journal: Proc. Amer. Math. Soc. 90 (1984), 649-652
MSC: Primary 54C56; Secondary 54C10, 55P55
DOI: https://doi.org/10.1090/S0002-9939-1984-0733420-7
MathSciNet review: 733420
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Abstract: It is shown that if $r:X \to Y$ is a refinable map between compacta and $Y$ is calm, then $r$ is a shape equivalence. As a corollary, if $r:X \to Y$ is a refinable map between compacta and either $X$ or $Y$ is ${S^n}$-like $(n \geqslant 1)$, then $r$ is a shape equivalence, where ${S^n}$ denotes the $n$-sphere.


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Keywords: Refinable map, shape equivalence, calm, FANR, AANR, movable
Article copyright: © Copyright 1984 American Mathematical Society