Linked from

The 14 pages that link to Open cover, each with the reason it gives.

• Compact 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.