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On approximation of homeomorphisms of a Cantor set

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Medynets K.

Fundamenta Mathematicae

2007

tom 194

nr 1

1-13

We continue the study of 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 by Bezuglyi, Dooley, Kwiatkowski and Medynets. 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 conjugacy 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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1 Fundamenta Mathematicae

1 Medynets K.

1 2007

Wyniki wyszukiwania

On approximation of homeomorphisms of a Cantor set