A function f:X→Yf: X\to Yf:X→Y between metric spaces (X,ρ)(X, \rho)(X,ρ) and (Y,σ)(Y,\sigma)(Y,σ) is an isometry if for all a,b∈Xa,b \in Xa,b∈X, σ(f(a),f(b))=ρ(a,b).\sigma(f(a), f(b)) = \rho(a,b).σ(f(a),f(b))=ρ(a,b). Two metric spaces are isometric if there exists an isometry between them.
Wikidata ID: Q740207