Generically there is but one self homeomorphism of the Cantor set

Akin, Ethan; Glasner, Eli; Weiss, Benjamin

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

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.

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