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Hereditarily indecomposable compacta do not admit expansive homeomorphisms

Author(s): Hisao Kato; Christopher G. Mouron
Journal: Proc. Amer. Math. Soc. 136 (2008), 3689-3696.
MSC (2000): Primary 54H20, 54F50; Secondary 54E40
Posted: May 15, 2008
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Abstract: A homeomorphism $ h:X\longrightarrow X$ is expansive provided that for some fixed $ c>0$ and every $ x, y\in X$ there exists an integer $ n$, dependent only on $ x$ and $ y$, such that d$ (h^n(x),h^n(y))>c$. It is shown that if $ X$ is a hereditarily indecomposable compactum, then $ h$ cannot be expansive.

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Additional Information:

Hisao Kato
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305 Japan
Email: hisakato@sakura.cc.tsukuba.ac.jp

Christopher G. Mouron
Affiliation: Department of Mathematics, The University of Alabama at Birmingham, Birmingham, Alabama 39254
Address at time of publication: Department of Mathematics and Computer Science, Rhodes College, Memphis, Tennessee 38112
Email: mouronc@rhodes.edu

DOI: 10.1090/S0002-9939-08-09316-7
PII: S 0002-9939(08)09316-7
Keywords: Expansive homeomorphism, hereditarily indecomposable continuum
Received by editor(s): January 18, 2007,
Received by editor(s) in revised form: August 3, 2007
Posted: May 15, 2008
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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