# Definition(s) > [!NOTE] Definition 1 (Distance Preserving Map) > Let $(X_{1},d_{1})$ and $(X_{2},d_{2})$ be [[Metrics|metric spaces]]. A distance preserving map from $(X_{1},d_{1})$ to $(X_{2},d_{2})$ is a map $f:X_{1}\to X_{2}$such that for all $P,Q\in X_{1},$ we have $d_{2}(f(P),f(Q))=d_{1}(P,Q).$ > [!Example] Example > An [[Isometry]] is a bijective distance preserving map. # Properties(s) # Application(s) **More examples**: # Bibliography