Topologies on the group of homeomorphisms of a Cantor set

Sergey Bezuglyi, Anthony H. Dooley, Jan Kwiatkowski

DOI: http://dx.doi.org/10.12775/TMNA.2006.013

Abstract


Let $\text{\rm Homeo}(\Omega)$ be the group of all homeomorphisms of a Cantor set
$\Omega$. We study topological properties of $\text{\rm Homeo}(\Omega)$ 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; minimal homeomorphisms; full groups; odometer

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