2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59755Let X be a real normed vector space and dim X \ge 2. Let d>0 be a fixed real number. We prove that if x,y \in X and ||x-y||/d is a rational number then there exists a finite set {x,y} \subseteq S(x,y) \subseteq X with the following property: for each strictly convex Y of dimension 2 each map from S(x,y) to Y preserving the distance d preserves the distance between x and y. It implies that each map from X to Y that preserves the distance d is an isometry.LaTeX 2.09, with a note that S(x,y) does not depend on YFunctional AnalysisMetric Geometry46B20text