Hereditarily indecomposable compacta do not admit expansive homeomorphisms
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- by Hisao Kato and Christopher G. Mouron PDF
- Proc. Amer. Math. Soc. 136 (2008), 3689-3696 Request permission
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 $\mbox {d}(h^n(x),h^n(y))>c$. It is shown that if $X$ is a hereditarily indecomposable compactum, then $h$ cannot be expansive.References
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Additional Information
- Hisao Kato
- Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305 Japan
- MR Author ID: 200384
- 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
- Received by editor(s): January 18, 2007
- Received by editor(s) in revised form: August 3, 2007
- Published electronically: May 15, 2008
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3689-3696
- MSC (2000): Primary 54H20, 54F50; Secondary 54E40
- DOI: https://doi.org/10.1090/S0002-9939-08-09316-7
- MathSciNet review: 2415056