KnowraOpen coverLinked fromLinked fromThe 14 pages that link to Open cover, each with the reason it gives.All 14Broader topic 3Related 10Narrower topic 1Compact spaceRelated: Compactness asks whether every such cover can be reduced to finitely many sets.Extreme value theoremRelated: Compactness is defined by requiring every open cover to have a finite subcover.Uniform continuityRelated: The Heine–Cantor theorem derives uniform continuity on compact spaces using finite subcovers.Heine–Borel theoremRelated: Finite subcovers are the defining test for compactness used in the theorem.Partition of unityNarrower topic: The partition is subordinate to this cover, with each function supported in one covering set.Tychonoff's theoremBroader topic: Finite subcovers define compactness in the theorem’s hypotheses and conclusion.Sheaf cohomologyRelated: Open covers organize local sections into Čech complexes that can compute cohomology.Heine–Cantor theoremRelated: Continuity neighborhoods cover the domain, and compactness reduces them to finitely many.Tube lemmaRelated: The proof covers the compact slice using product neighborhoods drawn from the given open set.Lindelöf's lemmaRelated: The lemma starts with an arbitrary open cover.Pavel AlexandrovBroader topic: The finite-subcover definition makes precise the compactness achieved by compactification.Seifert–Van Kampen theoremRelated: A common hypothesis ensures the union's topology is compatible with the calculation.Excision theoremRelated: The theorem's usual hypothesis places the removable subset inside the interior of another subspace.Family (mathematics)Broader topic: Compactness is defined by extracting finite subfamilies from open covers.