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Proceedings of the American Mathematical Society
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
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0733420-7
PII: S 0002-9939(1984)0733420-7
Keywords: Refinable map, shape equivalence, calm, FANR, AANR, movable
Article copyright: © Copyright 1984 American Mathematical Society