definition of Lipschitz map between metric spaces
Topics
About: metric space
The table of contents of this article
Starting Context
- The reader knows a definition of metric space.
- The reader knows a definition of map.
Target Context
- The reader will have a definition of Lipschitz map between metric spaces.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( T_1\): \(\in \{\text{ the metric spaces }\}\)
\( T_2\): \(\in \{\text{ the metric spaces }\}\)
\(*f\): \(: T_1 \to T_2\)
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Conditions:
\(\exists L \in \mathbb{R} \text{ such that } 0 \le L (\forall t_1, t_2 \in T_1 (dist (f (t_2), f (t_1)) \le L dist (t_2, t_1)))\)
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