KnowraHeine–Borel theoremLinked fromLinked fromThe 13 pages that link to Heine–Borel theorem, each with the reason it gives.All 13Broader topic 1Related 7Compared with 5Compact spaceRelated: It translates open-cover compactness into a familiar geometric test in Euclidean space.Extreme value theoremRelated: It makes the theorem’s compactness hypothesis concrete for subsets of the real line and Euclidean spaces.Bolzano–Weierstrass theoremRelated: The sequence theorem supplies the sequential compactness behind this characterization.Bounded setRelated: It makes boundedness part of a precise compactness test in finite-dimensional Euclidean spaces.Weierstrass theoremRelated: It turns the theorem’s abstract compactness condition into a familiar test for subsets of Euclidean space.Heine–Cantor theoremRelated: It provides a familiar test for the compact-domain hypothesis in Euclidean settings.Cantor's intersection theoremRelated: It lets the compact-space hypothesis be checked through geometry in Euclidean settings.