Table of Contents
- Distance Preserving Map
1. Definition
- A map \(f\colon X\to Y\) between metric spaces \(X, Y\), such that: \[ \forall a, b\in X, d_X(a, b) = d_Y(f(a), f(b)) \]
2. Global Isometry
- Isometric Isomorphism, Congruence Mapping, Rigid Transformation
- Bijective Isometry
3. Properties
- It is an injection