Short map

Definition
Suppose $$(X,d_X)$$ and $$(Y,d_Y)$$ are defining ingredient::metric spaces. A function $$f:X \to Y$$ is termed a short map if it satisfies the following:

$$\forall \ a,b \in X, d_Y(f(a),f(b)) \le d_X(a,b)$$.

Note that any short map is a Lipschitz-continuous map and is hence also a uniformly continuous map.

Stronger properties

 * Weaker than::Contraction

Weaker properties

 * Stronger than::Lipschitz-continuous map
 * Uniformly continuous map
 * Continuous map