KnowraBanach–Alaoglu theoremLinked fromLinked fromThe 8 pages that link to Banach–Alaoglu theorem, each with the reason it gives.All 8Broader topic 1Related 6Compared with 1Compact spaceRelated: It provides compactness in functional analysis where norm compactness often fails.Weak topologyRelated: It supplies compactness in a related topology when weak compactness is unavailable.Zorn's lemmaRelated: Choice-based compactness arguments, often through Tychonoff's theorem, underpin its general form.Tychonoff's theoremRelated: Its proof uses product compactness to establish compactness of dual-space balls.Eberlein–Šmulian theoremRelated: Its compactness supplies a central tool in proofs using the dual space.Krein–Milman theoremRelated: It supplies compact convex sets where Krein–Milman produces extreme points.