Generically there is but one self homeomorphism of the Cantor set
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- by Ethan Akin, Eli Glasner and Benjamin Weiss PDF
- Trans. Amer. Math. Soc. 360 (2008), 3613-3630 Request permission
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.References
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Additional Information
- Ethan Akin
- Affiliation: Mathematics Department, The City College, 137 Street and Convent Avenue, New York, New York 10031
- MR Author ID: 24025
- Email: ethanakin@earthlink.net
- Eli Glasner
- Affiliation: Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
- MR Author ID: 271825
- Email: glasner@math.tau.ac.il
- Benjamin Weiss
- Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
- MR Author ID: 181570
- Email: weiss@math.huji.ac.il
- Received by editor(s): April 26, 2006
- Published electronically: February 27, 2008
- Additional Notes: This research was supported by ISF grant # 1333/04.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3613-3630
- MSC (2000): Primary 22A05, 22D05; Secondary 54C40, 37E15
- DOI: https://doi.org/10.1090/S0002-9947-08-04450-4
- MathSciNet review: 2386239