KnowraBaire category theoremLinked fromLinked fromThe 14 pages that link to Baire category theorem, each with the reason it gives.All 14Related 12Compared with 2Banach spaceRelated: Its complete-metric-space form underlies several fundamental Banach-space theorems.Almost everywhereRelated: Its category-based notion of largeness contrasts with measure-based almost-everywhere truth.Complete metric spaceRelated: Completeness prevents the space from being exhausted by countably many thin subsets.Axiom of dependent choiceRelated: A standard proof uses dependent choice to construct nested closed sets with shrinking diameters.Weierstrass functionRelated: Related category arguments show that nowhere differentiability is widespread in spaces of continuous functions.Uncountable setRelated: It supports proofs that certain spaces or sets cannot be reduced to countable unions.Open mapping theoremRelated: Its category argument became the standard engine behind the theorem’s proof.Nikolai LuzinRelated: Category methods underpin the distinction between meagre sets and the large sets studied in Luzin’s work.Uniform boundedness principleRelated: Completeness supplies the category argument that converts pointwise bounds into a bound on a ball.Banach–Steinhaus theoremRelated: Completeness lets the proof show that some pointwise boundedness set contains an open ball.Martin's axiomRelated: Martin's axiom extends related category arguments to unions of fewer than continuum many sets.Axiom of countable choiceRelated: Standard proofs can use countable choice to select points from successive dense open sets.