2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72980Let $Homeo(Ω)$ 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 pagesDynamical Systems37B05; 37A40text