Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Heine–Borel_theorem> ?p ?o }
- Heine–Borel_theorem abstract "In the topology of metric spaces the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:For a subset S of Euclidean space Rn, the following two statements are equivalent:S is closed and boundedS is compact (that is, every open cover of S has a finite subcover).In the context of real analysis, the former property is sometimes used as the defining property of compactness. However, the two definitions cease to be equivalent when we consider subsets of more general metric spaces and in this generality only the latter property is used to define compactness. In fact, the Heine–Borel theorem for arbitrary metric spaces reads:A subset of a metric space is compact if and only if it is complete and totally bounded.".
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- Heine–Borel_theorem wikiPageWikiLink Arthur_Moritz_Schoenflies.
- Heine–Borel_theorem wikiPageWikiLink Arzelà–Ascoli_theorem.
- Heine–Borel_theorem wikiPageWikiLink Axiom_of_choice.
- Heine–Borel_theorem wikiPageWikiLink Axiom_of_dependent_choice.
- Heine–Borel_theorem wikiPageWikiLink Banach_space.
- Heine–Borel_theorem wikiPageWikiLink Bolzano–Weierstrass_theorem.
- Heine–Borel_theorem wikiPageWikiLink Boolean_prime_ideal_theorem.
- Heine–Borel_theorem wikiPageWikiLink Bounded_set.
- Heine–Borel_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Heine–Borel_theorem wikiPageWikiLink Category:Compactness_theorems.
- Heine–Borel_theorem wikiPageWikiLink Category:General_topology.
- Heine–Borel_theorem wikiPageWikiLink Category:Properties_of_topological_spaces.
- Heine–Borel_theorem wikiPageWikiLink Category:Theorems_in_real_analysis.
- Heine–Borel_theorem wikiPageWikiLink Cauchy_sequence.
- Heine–Borel_theorem wikiPageWikiLink Closed_set.
- Heine–Borel_theorem wikiPageWikiLink Compact_space.
- Heine–Borel_theorem wikiPageWikiLink Complete_metric_space.
- Heine–Borel_theorem wikiPageWikiLink Continuous_function.
- Heine–Borel_theorem wikiPageWikiLink Countable_set.
- Heine–Borel_theorem wikiPageWikiLink Cover_(topology).
- Heine–Borel_theorem wikiPageWikiLink Eduard_Heine.
- Heine–Borel_theorem wikiPageWikiLink Euclidean_space.
- Heine–Borel_theorem wikiPageWikiLink Fréchet_space.
- Heine–Borel_theorem wikiPageWikiLink Hausdorff_space.
- Heine–Borel_theorem wikiPageWikiLink Henri_Lebesgue.
- Heine–Borel_theorem wikiPageWikiLink Jean_Dieudonné.
- Heine–Borel_theorem wikiPageWikiLink Karl_Weierstrass.
- Heine–Borel_theorem wikiPageWikiLink Limit_point.
- Heine–Borel_theorem wikiPageWikiLink Metric_space.
- Heine–Borel_theorem wikiPageWikiLink Neighbourhood_(mathematics).
- Heine–Borel_theorem wikiPageWikiLink Nuclear_space.
- Heine–Borel_theorem wikiPageWikiLink Peter_Gustav_Lejeune_Dirichlet.
- Heine–Borel_theorem wikiPageWikiLink Pierre_Cousin.
- Heine–Borel_theorem wikiPageWikiLink Rational_number.
- Heine–Borel_theorem wikiPageWikiLink Real_analysis.
- Heine–Borel_theorem wikiPageWikiLink Salvatore_Pincherle.
- Heine–Borel_theorem wikiPageWikiLink Subset.
- Heine–Borel_theorem wikiPageWikiLink Topological_vector_space.
- Heine–Borel_theorem wikiPageWikiLink Topology.
- Heine–Borel_theorem wikiPageWikiLink Totally_bounded_space.
- Heine–Borel_theorem wikiPageWikiLink Uniform_continuity.
- Heine–Borel_theorem wikiPageWikiLink Uniform_space.
- Heine–Borel_theorem wikiPageWikiLink Émile_Borel.
- Heine–Borel_theorem wikiPageWikiLinkText "Heine–Borel theorem".
- Heine–Borel_theorem wikiPageWikiLinkText "Heine-Borel theorem".
- Heine–Borel_theorem wikiPageWikiLinkText "Heine–Borel property".
- Heine–Borel_theorem wikiPageWikiLinkText "Heine–Borel theorem".
- Heine–Borel_theorem wikiPageWikiLinkText "uniformly continuous".
- Heine–Borel_theorem id "3328".
- Heine–Borel_theorem id "p/b017100".
- Heine–Borel_theorem title "Borel-Lebesgue covering theorem".
- Heine–Borel_theorem title "proof of Heine-Borel theorem".
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- Heine–Borel_theorem subject Category:Articles_containing_proofs.
- Heine–Borel_theorem subject Category:Compactness_theorems.
- Heine–Borel_theorem subject Category:General_topology.
- Heine–Borel_theorem subject Category:Properties_of_topological_spaces.
- Heine–Borel_theorem subject Category:Theorems_in_real_analysis.
- Heine–Borel_theorem hypernym Equivalent.
- Heine–Borel_theorem type Organisation.
- Heine–Borel_theorem type Proof.
- Heine–Borel_theorem type Property.
- Heine–Borel_theorem type Redirect.
- Heine–Borel_theorem type Space.
- Heine–Borel_theorem type Theorem.
- Heine–Borel_theorem comment "In the topology of metric spaces the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:For a subset S of Euclidean space Rn, the following two statements are equivalent:S is closed and boundedS is compact (that is, every open cover of S has a finite subcover).In the context of real analysis, the former property is sometimes used as the defining property of compactness.".
- Heine–Borel_theorem label "Heine–Borel theorem".
- Heine–Borel_theorem sameAs Q253214.
- Heine–Borel_theorem sameAs مبرهنة_هاين-بوريل.
- Heine–Borel_theorem sameAs Teorema_de_Heine-Borel.
- Heine–Borel_theorem sameAs Satz_von_Heine-Borel.
- Heine–Borel_theorem sameAs Teorema_de_Heine-Borel.
- Heine–Borel_theorem sameAs Boreli-Lebesguei_teoreem.
- Heine–Borel_theorem sameAs Heinen–Borelin_lause.
- Heine–Borel_theorem sameAs Théorème_de_Borel-Lebesgue.
- Heine–Borel_theorem sameAs משפט_היינה-בורל.
- Heine–Borel_theorem sameAs Borel–Lebesgue-tétel.
- Heine–Borel_theorem sameAs Teorema_di_Heine-Borel.
- Heine–Borel_theorem sameAs ハイネ・ボレルの被覆定理.
- Heine–Borel_theorem sameAs 하이네-보렐_정리.
- Heine–Borel_theorem sameAs Stelling_van_Heine-Borel.
- Heine–Borel_theorem sameAs Twierdzenie_Heinego-Borela.
- Heine–Borel_theorem sameAs Teorema_de_Heine-Borel.
- Heine–Borel_theorem sameAs m.0g71c.
- Heine–Borel_theorem sameAs Лемма_Гейне_—_Бореля.
- Heine–Borel_theorem sameAs Борел-Лебегова_лема.
- Heine–Borel_theorem sameAs Heine–Borels_sats.
- Heine–Borel_theorem sameAs Лема_Гейне_—_Бореля.
- Heine–Borel_theorem sameAs Định_lý_Heine-Borel.