2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215479It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an $F_σ$-subset of a "smaller" dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces.5 pagesGeneral TopologyGeometric Topology54F45 (Primary), 55M10(Secondary)text