KnowraSequential compactnessLinked fromLinked fromThe 9 pages that link to Sequential compactness, each with the reason it gives.All 9Related 6Narrower topic 1Compared with 2Compact spaceCompared with: It matches open-cover compactness in metric spaces but can differ in general spaces.Bolzano–Weierstrass theoremNarrower topic: The theorem establishes this property for closed, bounded subsets of Euclidean space.Heine–Borel theoremRelated: In Euclidean spaces, this equivalent formulation connects the theorem to subsequence arguments.Tychonoff's theoremCompared with: It often differs from compactness in general spaces, so it cannot replace the theorem’s conclusion.Compact operatorRelated: In normed spaces, compact operators are characterized by subsequence convergence of bounded sequences.Weierstrass theoremRelated: This sequence formulation supplies the limit point needed in the standard proof.Axiom of countable choiceRelated: Some proofs extracting a subsequence from infinitely many successive choices invoke countable choice.Eberlein–Šmulian theoremRelated: The theorem identifies this sequential property with weak compactness for sets in Banach spaces.Cantor's intersection theoremRelated: In metric spaces, sequential compactness provides an alternative route to the nested-set conclusion.