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Metric map

In mathematical analysis, a metric map is a function between metric spaces that does not increase any distance. These maps are the morphisms in the category of metric spaces, Met. Such functions are always continuous functions. They are also called Lipschitz functions with Lipschitz constant 1, nonexpansive maps, nonexpanding maps, weak contractions, or…

Category of metric maps, Multivalued version & Examples

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Examples

Category of metric maps

Multivalued version

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Metric map

Nodes24
Edges23
Triples10
Avg. degree1.92
Density0.083333
Components1

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Metric map

Top relations

related to Examples · 5
Metric map → Consider, Euclidean, In, Lipschitz, Then
related to Category of metric maps · 4
Metric map → Lipschitz, Met, The, Thus
is a · 1
Metric map → function between metric spaces that does not increase any distance

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Important terminology

metric displaystyle map spaces function maps category met also lipschitz functions distance thus space mathematical called constant nonexpansive points leq

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Metric mapis afunction between metric spaces that does not increase any distance0.90text
Metric maprelated to Category of metric mapsThe0.60section
Metric maprelated to Category of metric mapsThus0.60section
Metric maprelated to Category of metric mapsMet0.60section
Metric maprelated to Category of metric mapsLipschitz0.60section
Metric maprelated to ExamplesConsider0.60section
Metric maprelated to ExamplesEuclidean0.60section
Metric maprelated to ExamplesThen0.60section
Metric maprelated to ExamplesIn0.60section
Metric maprelated to ExamplesLipschitz0.60section

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    Min side: 3
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