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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generically there is but one self homeomorphism of the Cantor set


Authors: Ethan Akin, Eli Glasner and Benjamin Weiss
Journal: Trans. Amer. Math. Soc. 360 (2008), 3613-3630
MSC (2000): Primary 22A05, 22D05; Secondary 54C40, 37E15
Published electronically: February 27, 2008
MathSciNet review: 2386239
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a self homeomorphism $ R$ of the Cantor set $ X$ and then show that its conjugacy class in the Polish group $ H(X)$ of all homeomorphisms of $ X$ forms a dense $ G_\delta$ subset of $ H(X)$. We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.


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Additional Information

Ethan Akin
Affiliation: Mathematics Department, The City College, 137 Street and Convent Avenue, New York, New York 10031
Email: ethanakin@earthlink.net

Eli Glasner
Affiliation: Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
Email: glasner@math.tau.ac.il

Benjamin Weiss
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
Email: weiss@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04450-4
PII: S 0002-9947(08)04450-4
Keywords: Rohlin property, group of homeomorphisms of the Cantor set, conjugacy class
Received by editor(s): April 26, 2006
Published electronically: February 27, 2008
Additional Notes: This research was supported by ISF grant # 1333/04.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.