On approximation of homeomorphisms of a Cantor set

Details On approximation of homeomorphisms of a Cantor set On approximation of homeomorphisms of a Cantor set

2005-10-03

arxiv.org/abs/math/0510032v2

Fundamenta Mathematicae 194 (2007), p.1-13

Mathematics

Dynamical Systems

12 pages: typos fixed

Scientific paper

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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