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- Pointclass abstract "In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open sets in some fixed collection of Polish spaces is a pointclass. (An open set may be seen as in some sense definable because it cannot be a purely arbitrary collection of points; for any point in the set, all points sufficiently close to that point must also be in the set.)Pointclasses find application in formulating many important principles and theorems from set theory and real analysis. Strong set-theoretic principles may be stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses (or sometimes larger ones) have regularity properties such as Lebesgue measurability (and indeed universal measurability), the property of Baire, and the perfect set property.".
- Pointclass wikiPageID "9304834".
- Pointclass wikiPageLength "6735".
- Pointclass wikiPageOutDegree "42".
- Pointclass wikiPageRevisionID "680519587".
- Pointclass wikiPageWikiLink Analytic_set.
- Pointclass wikiPageWikiLink Analytical_hierarchy.
- Pointclass wikiPageWikiLink Arithmetical_hierarchy.
- Pointclass wikiPageWikiLink Baire_space_(set_theory).
- Pointclass wikiPageWikiLink Boldface.
- Pointclass wikiPageWikiLink Borel_hierarchy.
- Pointclass wikiPageWikiLink Cantor_space.
- Pointclass wikiPageWikiLink Cartesian_product.
- Pointclass wikiPageWikiLink Category:Descriptive_set_theory.
- Pointclass wikiPageWikiLink Category:General_topology.
- Pointclass wikiPageWikiLink Class_(set_theory).
- Pointclass wikiPageWikiLink Closed_set.
- Pointclass wikiPageWikiLink Computable_set.
- Pointclass wikiPageWikiLink Continuous_function.
- Pointclass wikiPageWikiLink Descriptive_set_theory.
- Pointclass wikiPageWikiLink Determinacy.
- Pointclass wikiPageWikiLink Effective_descriptive_set_theory.
- Pointclass wikiPageWikiLink Emphasis_(typography).
- Pointclass wikiPageWikiLink F-sigma.
- Pointclass wikiPageWikiLink Fσ_set.
- Pointclass wikiPageWikiLink G-delta_set.
- Pointclass wikiPageWikiLink Gδ_set.
- Pointclass wikiPageWikiLink Homeomorphic.
- Pointclass wikiPageWikiLink Homeomorphism.
- Pointclass wikiPageWikiLink Hyperarithmetic_hierarchy.
- Pointclass wikiPageWikiLink Hyperarithmetical_theory.
- Pointclass wikiPageWikiLink Image_(mathematics).
- Pointclass wikiPageWikiLink Inverse_image.
- Pointclass wikiPageWikiLink Lebesgue_measure.
- Pointclass wikiPageWikiLink Open_set.
- Pointclass wikiPageWikiLink Oracle_machine.
- Pointclass wikiPageWikiLink Perfect_set.
- Pointclass wikiPageWikiLink Perfect_set_property.
- Pointclass wikiPageWikiLink Point_(geometry).
- Pointclass wikiPageWikiLink Point_(mathematics).
- Pointclass wikiPageWikiLink Polish_space.
- Pointclass wikiPageWikiLink Projective_hierarchy.
- Pointclass wikiPageWikiLink Proper_class.
- Pointclass wikiPageWikiLink Property_of_Baire.
- Pointclass wikiPageWikiLink Real_analysis.
- Pointclass wikiPageWikiLink Recursive_ordinal.
- Pointclass wikiPageWikiLink Recursive_set.
- Pointclass wikiPageWikiLink Set_(mathematics).
- Pointclass wikiPageWikiLink Set_theory.
- Pointclass wikiPageWikiLink Singleton_(mathematics).
- Pointclass wikiPageWikiLink Singleton_set.
- Pointclass wikiPageWikiLink Universally_measurable_set.
- Pointclass wikiPageWikiLink Wadge_degree.
- Pointclass wikiPageWikiLink Wadge_hierarchy.
- Pointclass wikiPageWikiLink Wadge_reducibility.
- Pointclass wikiPageWikiLink Yiannis_N._Moschovakis.
- Pointclass wikiPageWikiLink Zero-dimensional_space.
- Pointclass wikiPageWikiLink Zero_dimensional.
- Pointclass wikiPageWikiLinkText "Pointclass".
- Pointclass wikiPageWikiLinkText "pointclass".
- Pointclass wikiPageWikiLinkText "pointclass#Lightface pointclasses".
- Pointclass hasPhotoCollection Pointclass.
- Pointclass wikiPageUsesTemplate Template:Cite_book.
- Pointclass subject Category:Descriptive_set_theory.
- Pointclass subject Category:General_topology.
- Pointclass hypernym Collection.
- Pointclass type Book.
- Pointclass comment "In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open sets in some fixed collection of Polish spaces is a pointclass.".
- Pointclass label "Pointclass".
- Pointclass sameAs m.0283rrs.
- Pointclass sameAs Q7208299.
- Pointclass sameAs Q7208299.
- Pointclass wasDerivedFrom Pointclass?oldid=680519587.
- Pointclass isPrimaryTopicOf Pointclass.