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Polish space

In mathematics, a Polish space is a separable, completely metrizable topological space; i.e., a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians, such as Sierpiński, Kuratowski, Tarski and others.

Characters, Generalizations & Polish groups

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Overview

Properties

Characterization

Polish metric spaces

Generalizations

Polish groups

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Map overview Semantic statistics

Polish space

Nodes71
Edges70
Triples41
Avg. degree1.97
Density0.028169
Components1

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Polish space

Top relations

related to Polish groups · 14
Polish space → As, Baire, Baire-measurable, Banach, Borel, Examples, Firstly, Freudenthal, Hilbert, Kuratowski, Polish, Secondly, The, There
related to Properties · 7
Polish space → Bendixson, Cantor, Every Polish, Hilbert, Moreover, Polish, The
related to Suslin spaces · 7
Polish space → Hausdorff, Lusin, Mikhail Suslin, Polish, Suslin, The, Thus
related to Lusin spaces · 6
Polish space → Hausdorff, In, Lusin, Nikolai Lusin, Polish, There
is a · 3
Polish space → Lusin space.A subspace of a Lusin space is a Lusin space if and only if it is a Borel set.Any countable union or intersection of Lusin subspaces of a Hausdorff space is a Lusin…, separable, Suslin space if and only if it is a Suslin set
related to Polish metric spaces · 3
Polish space → Although Polish, An, Polish

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Important terminology

polish space spaces separable metric complete countable borel topological every lusin suslin metrizable open displaystyle set radon hausdorff topology particular

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polish spaceis aseparable0.90text
Polish spaceis aLusin space.A subspace of a Lusin space is a Lusin space if and only if it is a Borel set.Any countable union or intersection of Lusin subspaces of a Hausdorff space is a Lusin…0.90text
Polish spaceis aSuslin space if and only if it is a Suslin set0.90text
the open unit intervalinstance ofTopological spaces0.80text
Polish spacerelated to Lusin spacesHausdorff0.60section
Polish spacerelated to Lusin spacesLusin0.60section
Polish spacerelated to Lusin spacesNikolai Lusin0.60section
Polish spacerelated to Lusin spacesPolish0.60section
Polish spacerelated to Lusin spacesThere0.60section
Polish spacerelated to Lusin spacesIn0.60section
Polish spacerelated to Polish groupsPolish0.60section
Polish spacerelated to Polish groupsThere0.60section

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