Topologies on the group of homeomorphisms of a Cantor set
Keywords
Cantor set, minimal homeomorphisms, full groups, odometerAbstract
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.Downloads
Published
2006-06-01
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1.
BEZUGLYI, Sergey, DOOLEY, Anthony H. and KWIATKOWSKI, Jan. Topologies on the group of homeomorphisms of a Cantor set. Topological Methods in Nonlinear Analysis. Online. 1 June 2006. Vol. 27, no. 2, pp. 299 - 331. [Accessed 14 February 2025].
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