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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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Published in: | Proceedings of the American Mathematical Society 2008-10, Vol.136 (10), p.3689-3696 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/S0002-9939-08-09316-7 |