2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110290We describe a self-homeomorphism $R$ of the Cantor set $X$ and then show that its conjugacy class in the Polish group $H(X)$ of all homeomorphisms of $X$ forms a dense $G_δ$ subset of $H(X)$. We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.Dynamical SystemsGroup Theory22A05text