Short map: Difference between revisions
(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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Note that any short map is a [[Lipschitz-continuous map]] and is hence also a [[uniformly continuous map]]. | 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 than::Contraction]] | |||
===Weaker properties=== | |||
* [[Stronger than::Lipschitz-continuous map]] | |||
* [[Stronger than::Uniformly continuous map of metric spaces|Uniformly continuous map]] | |||
* [[Stronger than::Continuous map of metric spaces|Continuous map]] | |||
Latest revision as of 23:30, 24 November 2008
Definition
Suppose and are metric spaces. A function is termed a short map if it satisfies the following:
.
Note that any short map is a Lipschitz-continuous map and is hence also a uniformly continuous map.