Topologies on the group of homeomorphisms of a Cantor set

Bezuglyi, Sergey; Dooley, Anthony H.; Kwiatkowski, Jan

Topologies on the group of homeomorphisms of a Cantor set

Authors

Bezuglyi, Sergey

Dooley, Anthony H.

Kwiatkowski, Jan

Description

Let $Homeo(Ω)$ be the group of all homeomorphisms of a Cantor set $Ω$. We study topological properties of $Homeo(Ω)$ and its subsets with respect to the uniform $(τ)$ and weak $(τ_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $τ$ and $τ_w$ are found.
33 pages