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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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The nonexistence of expansive homeomorphisms of $1$-dimensional compact ANRs
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by Hisao Kato PDF
Proc. Amer. Math. Soc. 108 (1990), 267-269 Request permission

Abstract:

It is well known that if $X$ is an arc or a circle, then there is no expansive homeomorphism on $X$ (see [2] and [3]). In this note, we show that if $X$ is a Peano continuum which has a neighborhood $M$ such that ${\text {cl}}\left ( M \right )$ is a $1$-dimensional AR, then there is no expansive homeomorphism on $X$ . In particular, no $1$-dimensional compact ANR admits an expansive homeomorphism.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 267-269
  • MSC: Primary 54E40; Secondary 54F50, 54H20, 58F15
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0991698-1
  • MathSciNet review: 991698