About: Limit point compact

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In mathematics, a topological space X is said to be limit point compact or weakly countably compact if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:WikicatPropertiesOfTopologicalSpaces
rdfs:label	Limit point compact (en) 극한점 콤팩트 공간 (ko) Слабко зліченно компактний простір (uk)
rdfs:comment	In mathematics, a topological space X is said to be limit point compact or weakly countably compact if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent. (en) 일반위상수학에서 극한점 콤팩트 공간(Limit point compact space, 極限點 compact 空間) 또는 집적점 콤팩트 공간(集積點 compact 空間) 또는 약가산 콤팩트 공간(weakly countably compact space, 弱可算 compact 空間)은 콤팩트 공간의 개념의 변형 가운데 하나이다. (ko) Топологічний простір X називається слабко зліченно компактним, якщо кожна нескінченна підмножина X має граничну точку в X. (uk)
dcterms:subject	Properties of topological spaces Compactness (mathematics)
Wikipage page ID	9861462 (xsd:integer)
Wikipage revision ID	1034618374 (xsd:integer)
Link from a Wikipage to another Wikipage	Prentice Hall Compact space Compact spaces Order topology Properties of topological spaces Pseudocompact Compactness (mathematics) Cardinal function Tietze extension theorem Countably compact space Counterexamples in Topology T0 space Cocountable topology Discrete topology Metric space Limit point Topological space Sequentially compact space T1 space Odd-even topology Countable complement topology Indiscrete topology Sequential compactness
sameAs	Limit point compact Limit point compact Limit point compact Limit point compact Limit point compact Limit point compact
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:ISBN dbt:Reflist dbt:PlanetMath_attribution
id	1234 (xsd:integer)
title	Weakly countably compact (en)
has abstract	In mathematics, a topological space X is said to be limit point compact or weakly countably compact if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent. (en) 일반위상수학에서 극한점 콤팩트 공간(Limit point compact space, 極限點 compact 空間) 또는 집적점 콤팩트 공간(集積點 compact 空間) 또는 약가산 콤팩트 공간(weakly countably compact space, 弱可算 compact 空間)은 콤팩트 공간의 개념의 변형 가운데 하나이다. (ko) Топологічний простір X називається слабко зліченно компактним, якщо кожна нескінченна підмножина X має граничну точку в X. (uk)
prov:wasDerivedFrom	wikipedia-en:Limit_point_compact?oldid=1034618374&ns=0
page length (characters) of wiki page	5897 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Limit_point_compact
is Link from a Wikipage to another Wikipage of	Appert topology Compact space Idempotent relation Weakly countably compact K-topology Countably compact space Cocountable topology Eberlein–Šmulian theorem Weakly compact Limit point compactness Ultraconnected space Sequentially compact space Limit point compact space
is Wikipage redirect of	Weakly countably compact Limit point compactness Limit point compact space
is foaf:primaryTopic of	wikipedia-en:Limit_point_compact

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