2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145909We prove that two homogeneous ultra-metric spaces $X,Y$ are coarsely equivalent if and only if $\mathrm{Ent}^\sharp(X)=\mathrm{Ent}^\sharp(Y)$ where $\mathrm{Ent}^\sharp(X)$ is the so-called sharp entropy of $X$. This classification implies that each homogeneous proper ultra-metric space is coarsely equivalent to the anti-Cantor set $2^{<ω}$. For the proof of these results we develop a technique of towers which can have an independent interest.Geometric TopologyGeneral Topology54E35; 54E40text