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- Polish_space abstract "In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, 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 — Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations. Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory.Common examples of Polish spaces are the real line, any separable Banach space, the Cantor space, and Baire space. Additionally, some spaces that are not complete metric spaces in the usual metric may be Polish; e.g., the open interval (0, 1) is Polish.Between any two uncountable Polish spaces, there is a Borel isomorphism; that is, a bijection that preserves the Borel structure. In particular, every uncountable Polish space has the cardinality of the continuum.Lusin spaces, Suslin spaces, and Radon spaces are generalizations of Polish spaces.".
- Polish_space wikiPageID "396622".
- Polish_space wikiPageLength "7483".
- Polish_space wikiPageOutDegree "57".
- Polish_space wikiPageRevisionID "698456421".
- Polish_space wikiPageWikiLink Alfred_Tarski.
- Polish_space wikiPageWikiLink Automatic_continuity.
- Polish_space wikiPageWikiLink Baire_space_(set_theory).
- Polish_space wikiPageWikiLink Banach_space.
- Polish_space wikiPageWikiLink Bijection.
- Polish_space wikiPageWikiLink Borel_equivalence_relation.
- Polish_space wikiPageWikiLink Borel_isomorphism.
- Polish_space wikiPageWikiLink Cantor_space.
- Polish_space wikiPageWikiLink Cardinality_of_the_continuum.
- Polish_space wikiPageWikiLink Category:Descriptive_set_theory.
- Polish_space wikiPageWikiLink Category:General_topology.
- Polish_space wikiPageWikiLink Category:Science_and_technology_in_Poland.
- Polish_space wikiPageWikiLink Complete_metric_space.
- Polish_space wikiPageWikiLink Completely_metrizable_space.
- Polish_space wikiPageWikiLink Countable_set.
- Polish_space wikiPageWikiLink Dense_set.
- Polish_space wikiPageWikiLink Descriptive_set_theory.
- Polish_space wikiPageWikiLink Determinacy.
- Polish_space wikiPageWikiLink Disjoint_union.
- Polish_space wikiPageWikiLink Forgetful_functor.
- Polish_space wikiPageWikiLink General_topology.
- Polish_space wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Polish_space wikiPageWikiLink Gδ_set.
- Polish_space wikiPageWikiLink Hausdorff_space.
- Polish_space wikiPageWikiLink Homeomorphism.
- Polish_space wikiPageWikiLink Interval_(mathematics).
- Polish_space wikiPageWikiLink Kazimierz_Kuratowski.
- Polish_space wikiPageWikiLink Laurent_Schwartz.
- Polish_space wikiPageWikiLink Metric_space.
- Polish_space wikiPageWikiLink Metrization_theorem.
- Polish_space wikiPageWikiLink Nicolas_Bourbaki.
- Polish_space wikiPageWikiLink Pavel_Alexandrov.
- Polish_space wikiPageWikiLink Perfect_set.
- Polish_space wikiPageWikiLink Perfect_set_property.
- Polish_space wikiPageWikiLink Polish_group.
- Polish_space wikiPageWikiLink Polish_space.
- Polish_space wikiPageWikiLink Probability_theory.
- Polish_space wikiPageWikiLink Property_of_Baire.
- Polish_space wikiPageWikiLink Radon_measure.
- Polish_space wikiPageWikiLink Radon_space.
- Polish_space wikiPageWikiLink Real_line.
- Polish_space wikiPageWikiLink Separable_space.
- Polish_space wikiPageWikiLink Springer_Science+Business_Media.
- Polish_space wikiPageWikiLink Suslin_operation.
- Polish_space wikiPageWikiLink Suslin_representation.
- Polish_space wikiPageWikiLink Topological_game.
- Polish_space wikiPageWikiLink Topological_space.
- Polish_space wikiPageWikiLink Uncountable_set.
- Polish_space wikiPageWikiLink Wacław_Sierpiński.
- Polish_space wikiPageWikiLinkText "Lusin space".
- Polish_space wikiPageWikiLinkText "Luzin spaces".
- Polish_space wikiPageWikiLinkText "Polish Space".
- Polish_space wikiPageWikiLinkText "Polish space #Lusin spaces".
- Polish_space wikiPageWikiLinkText "Polish space".
- Polish_space wikiPageWikiLinkText "Polish topological space".
- Polish_space wikiPageWikiLinkText "Polish".
- Polish_space wikiPageWikiLinkText "Polish_space#Suslin_spaces".
- Polish_space wikiPageWikiLinkText "complete separable metric space".
- Polish_space wikiPageUsesTemplate Template:Cite_book.
- Polish_space wikiPageUsesTemplate Template:Main.
- Polish_space wikiPageUsesTemplate Template:Reflist.
- Polish_space subject Category:Descriptive_set_theory.
- Polish_space subject Category:General_topology.
- Polish_space subject Category:Science_and_technology_in_Poland.
- Polish_space type Redirect.
- Polish_space comment "In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, 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 — Sierpiński, Kuratowski, Tarski and others.".
- Polish_space label "Polish space".
- Polish_space sameAs Q1207972.
- Polish_space sameAs Polnischer_Raum.
- Polish_space sameAs Espace_polonais.
- Polish_space sameAs Spazio_polacco.
- Polish_space sameAs ポーランド空間.
- Polish_space sameAs 폴란드_공간.
- Polish_space sameAs Poolse_ruimte.
- Polish_space sameAs Przestrzeń_polska.
- Polish_space sameAs Spassi_polonèis.
- Polish_space sameAs m.023cmf.
- Polish_space sameAs Q1207972.
- Polish_space wasDerivedFrom Polish_space?oldid=698456421.
- Polish_space isPrimaryTopicOf Polish_space.