Topologies on the group of homeomorphisms of a Cantor set

Sergey Bezuglyi; Anthony H. Dooley; Jan Kwiatkowski

Topologies on the group of homeomorphisms of a Cantor set

Dynamical Systems 2007-05-23 v2

Authors: Sergey Bezuglyi , Anthony H. Dooley , Jan Kwiatkowski

Abstract

Let $Homeo(\Omega)$ 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 $(\tau)$ and weak $(\tau_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $\tau$ and $\tau_w$ are found.

Keywords

cantor set homeomorphism group uniform topology weak topology odometer aperiodic minimal homeomorphism

Cite

@article{arxiv.math/0410507,
  title  = {Topologies on the group of homeomorphisms of a Cantor set},
  author = {Sergey Bezuglyi and Anthony H. Dooley and Jan Kwiatkowski},
  journal= {arXiv preprint arXiv:math/0410507},
  year   = {2007}
}

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33 pages

Topologies on the group of homeomorphisms of a Cantor set

Abstract

Keywords

Cite

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