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Hereditarily Indecomposable Compacta Do Not Admit Expansive Homeomorphisms

A homeomorphism h: X → X is expansive provided that for some fixed c > 0 and every x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x), hⁿ(y)) > c. It is shown that if X is a hereditarily indecomposable compactum, then h cannot be expansive.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-10, Vol.136 (10), p.3689-3696
Main Authors: Kato, Hisao, Mouron, Christopher G.
Format: Article
Language:English
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Summary:A homeomorphism h: X → X is expansive provided that for some fixed c > 0 and every x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x), hⁿ(y)) > c. It is shown that if X is a hereditarily indecomposable compactum, then h cannot be expansive.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-08-09316-7