TY - JOUR AU - Bezuglyi, Sergey AU - Dooley, Anthony H. AU - Kwiatkowski, Jan PY - 2006/06/01 Y2 - 2024/03/29 TI - Topologies on the group of homeomorphisms of a Cantor set JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 27 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2006.013 SP - 299 - 331 AB - 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 subsetswith respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. Theclasses of odometers and periodic, aperiodic, minimal, rank 1 homeomorphismsare considered and the closures of those classes in $\tau$ and $\tau_w$ arefound. ER -