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Short map

From Topospaces

Revision as of 23:17, 24 November 2008 by Vipul (talk | contribs) (New page: ==Definition== Suppose <math>(X,d_X)</math> and <math>(Y,d_Y)</math> are defining ingredient::metric spaces. A function <math>f:X \to Y</math> is termed a '''short map''' if it satisf...)

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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:

$\forall a, b \in X, d_{Y} (f (a), f (b)) \leq d_{X} (a, b)$ .

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

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