Isometry

Definition: Isometry

Let $(X,d_X)$ and $(Y,d_Y)$ be metric spaces.

An isometry or distance-preserving map from $(X,d_X)$ to $(Y,d_Y)$ is a function $f$ such that for all $a,b\in X$

$$d_X(a,b)=d_Y(f(a),f(b))$$