1071: Lipschitz Map Between Metric Spaces

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definition of Lipschitz map between metric spaces

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Topics

About: metric space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description

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Starting Context

• The reader knows a definition of metric space.
• The reader knows a definition of map.

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Target Context

• The reader will have a definition of Lipschitz map between metric spaces.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$T_1$: $\in \{\text{ the metric spaces }\}$
$T_2$: $\in \{\text{ the metric spaces }\}$
$\ast f$: $:T_1\to T_2$
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Conditions:
$\mathrm{\exists }L\in \mathbb{R}\text{ such that }0\le L(\mathrm{\forall }{t}_1,t_2\in T_1(dist(f(t_2),f(t_1))\le dist(t_2,t_1)))$
//

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References

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