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Generically there is but one self homeomorphism of the Cantor set

Ethan Akin·Eli Glasner·Benjamin Weiss
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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 $G_δ$ 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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Ethan Akin, Eli Glasner, Benjamin Weiss. 2006-03-22. Generically there is but one self homeomorphism of the Cantor set. https://arxiv.org/abs/math/0603538

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