Topologies on the group of homeomorphisms of a Cantor set

Sergey Bezuglyi, Anthony H. Dooley, Jan Kwiatkowski

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)299-332
JournalTopological Methods in Nonlinear Analysis
Volume27
Issue number2
Publication statusPublished - Jun 2006

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