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Statements

Subject Item
dbr:Limit_point_compact
rdf:type
yago:Relation100031921 yago:Property113244109 yago:Possession100032613 yago:Abstraction100002137 yago:WikicatPropertiesOfTopologicalSpaces
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극한점 콤팩트 공간 Слабко зліченно компактний простір Limit point compact
rdfs:comment
Топологічний простір X називається слабко зліченно компактним, якщо кожна нескінченна підмножина X має граничну точку в X. 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. 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.
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dbr:Discrete_topology dbr:Sequentially_compact_space dbr:Counterexamples_in_Topology dbr:Pseudocompact dbr:Indiscrete_topology dbr:Cocountable_topology dbr:Countable_complement_topology dbr:Tietze_extension_theorem dbr:Topological_space dbr:Compact_space dbr:Compact_spaces dbr:Odd-even_topology dbr:Prentice_Hall dbr:Limit_point dbr:T1_space dbr:Order_topology dbr:Metric_space dbc:Compactness_(mathematics) dbr:Sequential_compactness dbr:T0_space dbc:Properties_of_topological_spaces dbr:Cardinal_function dbr:Countably_compact_space
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1234
dbp:title
Weakly countably compact
dbo:abstract
Топологічний простір X називається слабко зліченно компактним, якщо кожна нескінченна підмножина X має граничну точку в X. 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. 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.
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wikipedia-en:Limit_point_compact