On approximation of homeomorphisms of a Cantor set
On approximation of homeomorphisms of a Cantor set
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关于康托集同胚的逼近
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发表时间：
2005
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通讯作者：
K. Medynets
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作者：
K. Medynets
本文继续研究由Bezuglyi，Dooley，Kwiatkowski和Medynets开始的关于一致拓扑τ的Cantor集X的所有同胚的群Homeo（X）的拓扑性质.证明了周期同胚集在Homeo（X）中是τ -稠密的，并由此推出拓扑群（Homeo（X），τ）具有Rokhlin性质，即，在Homeo（X）中存在一个共轭类为τ -稠密的同胚。我们还证明了对于任意同胚T，拓扑全群[[T ]]在全群[T ]中是τ -稠密的。
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 ].