Short map

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Definition

Suppose (X,d_X) and (Y,d_Y) are 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.

Relation with other properties

Stronger properties

Weaker properties