Generically there is but one self homeomorphism of the cantor set

Ethan Akin; Eli Glasner; Benjamin Weiss

doi:10.1090/S0002-9947-08-04450-4

Generically there is but one self homeomorphism of the cantor set

Ethan Akin^*, Eli Glasner, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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 Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.

Original language	English
Pages (from-to)	3613-3630
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	360
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-08-04450-4
State	Published - Jul 2008

Keywords

Conjugacy class
Group of homeomorphisms of the cantor set
Rohlin property

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10.1090/S0002-9947-08-04450-4

Cite this

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title = "Generically there is but one self homeomorphism of the cantor set",

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 Gδ 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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AB - 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 Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.

KW - Conjugacy class

KW - Group of homeomorphisms of the cantor set

KW - Rohlin property

UR - https://www.scopus.com/pages/publications/67649997185

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Generically there is but one self homeomorphism of the cantor set

Abstract

Keywords

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