Generically there is but one self homeomorphism of the Cantor set

Details Generically there is but one self homeomorphism of the Cantor set Generically there is but one self homeomorphism of the Cantor set

2006-03-22

arxiv.org/abs/math/0603538v1

Mathematics

Dynamical Systems

Scientific paper

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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