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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.)

Attributes	Values
rdf:type	book
rdfs:label	점류 (ko) Pointclass (en)
rdfs:comment	집합론에서 점류(點類, 영어: pointclass)는 어떤 구체적 범주(예를 들어, 폴란드 공간들의 범주)의 각 대상에 대하여 그 부분 집합들의 집합족을 대응시키며, 특정 함수 아래의 원상에 대하여 닫혀 있는 구조이다. (ko) 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.) (en)
dct:subject	Descriptive set theory General topology
Wikipage page ID	9304834 (xsd:integer)
Wikipage revision ID	1088051902 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Proper class Boldface Determinacy Homeomorphic Descriptive set theory Real analysis Continuous function Analytic set Analytical hierarchy Oracle machine G-delta set Arithmetical hierarchy Closed set Computable set Perfect set Descriptive set theory Lebesgue measure F-sigma Projective hierarchy Baire space (set theory) Hyperarithmetical theory General topology Effective descriptive set theory Borel hierarchy Polish space Open set Cantor space Recursive ordinal Set (mathematics) Set theory Perfect set property Universally measurable set Inverse image Property of Baire Wadge degree Yiannis Moschovakis Hyperarithmetic hierarchy Point (mathematics) Singleton set Wadge reducibility Zero dimensional
Link from a Wikipage to an external page	https://archive.org/details/descriptivesetth0000mosc
sameAs	Pointclass Pointclass Pointclass Pointclass
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Short_description dbt:Pointclasses
has 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. (en) 집합론에서 점류(點類, 영어: pointclass)는 어떤 구체적 범주(예를 들어, 폴란드 공간들의 범주)의 각 대상에 대하여 그 부분 집합들의 집합족을 대응시키며, 특정 함수 아래의 원상에 대하여 닫혀 있는 구조이다. (ko)
gold:hypernym	Collection
prov:wasDerivedFrom	wikipedia-en:Pointclass?oldid=1088051902&ns=0
page length (characters) of wiki page	7074 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pointclass
is Link from a Wikipage to another Wikipage of	Prewellordering Ω-logic Determinacy Descriptive set theory Moschovakis coding lemma Adequate pointclass Wadge hierarchy Difference hierarchy Set theory Boldface pointclass Scale (descriptive set theory) Uniformization (set theory) Lightface Lightface pointclass Point class Boldface (mathematics) Boldface hierarchy Lightface hierarchy Pointclasses
is Wikipage redirect of	Boldface pointclass Lightface Lightface pointclass Boldface (mathematics) Boldface hierarchy Lightface hierarchy Pointclasses
is foaf:primaryTopic of	wikipedia-en:Pointclass

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