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Polish space

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A separable topologically complete space. Polish spaces form a natural frame of descriptive set theory. The fundamental Polish space $ \mathbf I $ of irrationals is homeomorphic to the Baire space $ \mathbf N ^ {\mathbf N} $( often denoted by $ \omega ^ \omega $ by those logicians who identify $ \mathbf N $ and the first infinite ordinal number $ \omega $).

A Suslin space is a continuous image of a Polish space.

How to Cite This Entry:
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51151

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Polish spaceencyclopedia_of_mathematics Polish spaceencyclopedia_of_mathematics

Citations

Separable spaceoutgoing citation Descriptive set theoryoutgoing citation Baire spaceoutgoing citation Complete metric spaceoutgoing citation Ordinal numberoutgoing citation Wijsman convergenceincoming citation Large deviationsincoming citation Measureincoming citation Convergence of measuresincoming citation Sierpiński gameincoming citation Luzin theoremincoming citation Luzin separability principlesincoming citation Vague topologyincoming citation Skorokhod spaceincoming citation Spacesincoming citation

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discussesarticle:eom--polish-space--15428aa6c1 -> concept:polish-spaceconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

discussesarticle:eom--suslin-space--2e7ede1015 -> concept:polish-spaceconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:polish-space -> concept:separable-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:polish-space -> concept:descriptive-set-theoryconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:polish-space -> concept:baire-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:polish-space -> concept:complete-metric-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:polish-space -> concept:ordinal-numberconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:wijsman-convergence -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:large-deviations -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:measure -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:convergence-of-measures -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:sierpinski-game -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:luzin-theorem -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:luzin-separability-principles -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:vague-topology -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:skorokhod-space -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:spaces -> concept:polish-spaceconfidence: 1.00 - provenance: article backlink extractionreviewed

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