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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A remark on refinable maps and calmness
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by Hisao Kato PDF
Proc. Amer. Math. Soc. 90 (1984), 649-652 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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