Heine–Borel theorem
In real analysis 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 bounded
* S is compact, that is, every open cover of S has a finite subcover.
Arzelà–Ascoli theoremBanach–Alaoglu theoremBolzano–Weierstrass theoremBorel-Lebesgue theoremCantor's intersection theoremCantor setCauchy sequenceCompact spaceComplete metric spaceComputable analysisCousin's theoremEduard HeineEquicontinuityExtreme value theoremF. Riesz's theoremFinite subdivision ruleFroda's theoremGeneral topologyHaar waveletHeine-BorelHeine-Borel-Lebesgue theoremHeine-Borel TheoremHeine-Borel covering theoremHeine-Borel propertyHeine-Borel theoremHeine-borelHeine-borel theoremHeine Borel theoremHeine borelHeine borel theoremHeine–Borel propertyLeast-upper-bound propertyList of eponyms (A–K)List of general topology topicsList of mathematical proofsList of misnamed theoremsList of real analysis topicsList of theoremsList of things named after Eduard HeineLocally compact space
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Heine–Borel theorem
In real analysis 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 bounded
* S is compact, that is, every open cover of S has a finite subcover.
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Em matemática, o teorema de He ...... mente se é fechado e limitado.
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En el análisis matemático, el ...... rd Bolzano y Karl Weierstrass.
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En matemàtiques, el teorema de ...... rd Bolzano i Karl Weierstrass.
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En topologie de ℝn, le théorèm ...... valable en dimension infinie.
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Heine-Borels sats eller Heine- ...... utgör ett och är sluten och .
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In de wiskundige analyse, maar ...... eelverzameling compleet en is.
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In matematica, in particolare ...... ci Eduard Heine e Émile Borel.
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In real analysis the Heine–Bor ...... er of S has a finite subcover.
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Twierdzenie Heinego-Borela cha ...... est jednak Heinemu i Borelowi.
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Леммой Гейне — Бореля (а также ...... (или леммой Бореля — Лебега).
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p/b017100
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title
Borel-Lebesgue covering theorem
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Em matemática, o teorema de He ...... mente se é fechado e limitado.
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En el análisis matemático, el ...... nuncia de la siguiente manera:
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En matemàtiques, el teorema de ...... rd Bolzano i Karl Weierstrass.
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En topologie de ℝn, le théorèm ...... r la réciproque est immédiate.
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Heine-Borels sats eller Heine- ...... are form av Heine-Borels sats:
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In de wiskundige analyse, maar ...... dat wil zeggen dat compact is.
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In matematica, in particolare ...... ci Eduard Heine e Émile Borel.
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In real analysis the Heine–Bor ...... er of S has a finite subcover.
@en
Twierdzenie Heinego-Borela cha ...... est jednak Heinemu i Borelowi.
@pl
Леммой Гейне — Бореля (а также ...... (или леммой Бореля — Лебега).
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Heine–Borel theorem
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Heine–Borels sats
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Satz von Heine-Borel
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Stelling van Heine-Borel
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Teorema de Heine-Borel
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Teorema de Heine-Borel
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Teorema de Heine-Borel
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Teorema di Heine-Borel
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Théorème de Borel-Lebesgue
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Twierdzenie Heinego-Borela
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