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29 March 2024
 
  » arxiv » math.DS/0410507

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Topologies on the group of homeomorphisms of a Cantor set
Sergey Bezuglyi ; Anthony H. Dooley ; Jan Kwiatkowski ;
Date 23 Oct 2004
Subject Dynamical Systems MSC-class: 37B05; 37A40 | math.DS
AbstractLet $Homeo(Omega)$ be the group of all homeomorphisms of a Cantor set $Omega$. We study topological properties of $Homeo(Omega)$ and its subsets with respect to the uniform $( au)$ and weak $( au_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $ au$ and $ au_w$ are found.
Source arXiv, math.DS/0410507
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