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On approximation of homeomorphisms of a Cantor set

Konstantin Medynets
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Abstract

We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on the group of homeomorphisms of a Cantor set, ArXiv e-print math.DS/0410507, 2004). We prove that the set of periodic homeomorphisms is tau-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), tau) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugate class is tau-dense in Homeo(X). We also show that for any homeomorphism T the topological full group [[T]] is tau-dense in the full group [T].

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Konstantin Medynets. 2007-01-24. On approximation of homeomorphisms of a Cantor set. https://arxiv.org/abs/math/0510032

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