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Heine–Borel theorem

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In real analysis in mathematics, the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S {\displaystyle S} of Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , the following two statements are equivalent: S {\displaystyle S} is compact, that is, every open…

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