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Metrizable space

In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X,\tau )} is said to be metrizable if there is a metric d : X × X → [ 0 , ∞ ) {\displaystyle d:X\times X\to [0,\infty )} such that the topology induced by d {\displaystyle…

Examples, Metrization theorems & Properties

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Properties

Metrization theorems

Examples

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Metrizable space

Nodes56
Edges55
Triples7
Avg. degree1.96
Density0.035714
Components1

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Metrizable space

Top relations

related to Properties · 6
Metrizable space → For, Hausdorff, However, Metrizable, This, Tychonoff
is a · 1
Metrizable space → topological space that is homeomorphic to a metric space

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Important terminology

metrizable space hausdorff metric topological topology metrization theorem locally homeomorphic displaystyle second-countable theorems also paracompact spaces example every regular smirnov

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Metrizable spaceis atopological space that is homeomorphic to a metric space0.90text
Metrizable spacerelated to PropertiesMetrizable0.60section
Metrizable spacerelated to PropertiesFor0.60section
Metrizable spacerelated to PropertiesHausdorff0.60section
Metrizable spacerelated to PropertiesTychonoff0.60section
Metrizable spacerelated to PropertiesHowever0.60section
Metrizable spacerelated to PropertiesThis0.60section

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    Min side: 3
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