On approximation of homeomorphisms of a Cantor set
نویسنده
چکیده
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 τ , which was started in [B-K 1], [B-D-K 1; 2], [B-D-M], and [M]. We prove that the set of periodic homeomorphisms is τ -dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), τ) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugate class is τ -dense in Homeo(X). We also show that for any homeomorphism T the topological full group [[T ]] is τ -dense in the full group [T ].
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