2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63632It is shown that each continuous transformation $h$ from Euclidean $m$-space ($m>1$) into Euclidean $n$-space that preserves the equality of distances (that is, fulfils the implication $|x-y|=|z-w|\Rightarrow|h(x)-h(y)|=|h(z)-h(w)|$) is a similarity map. The case of equal dimensions already follows from the Beckman--Quarles Theorem.5 pagesMetric GeometryGeneral Topology51F20; 51F25; 15A04text