KnowraBanach–Steinhaus theoremLinked fromLinked fromThe 6 pages that link to Banach–Steinhaus theorem, each with the reason it gives.All 6Broader topic 1Related 3Compared with 2Banach spaceRelated: The theorem turns pointwise control into a uniform bound using completeness.Axiom of dependent choiceRelated: In common foundations, dependent choice supplies the countable recursive constructions used in its proof.Stefan BanachRelated: The theorem’s name records Banach’s role in its development with Steinhaus.Fredholm alternativeCompared with: Unlike the alternative, it controls families of operators rather than solvability of one equation.Uniform boundedness principleCompared with: This theorem is also widely known by this name, especially in functional analysis.Lwów School of MathematicsBroader topic: This foundational result emerged from the school’s work and remains central to analysis.