KnowraOpen mapping theoremLinked fromLinked fromThe 8 pages that link to Open mapping theorem, each with the reason it gives.All 8Broader topic 2Related 6Banach spaceRelated: Completeness of both spaces is essential to the conclusion.Functional analysisRelated: It yields continuity of inverse maps under standard completeness assumptions.Baire category theoremRelated: Completeness and Baire category yield the neighborhood needed to prove openness.Hahn–Banach theoremRelated: It is another central Banach-space theorem, but concerns maps between spaces rather than extending functionals.Uniform boundedness principleRelated: It is a central companion theorem derived from the same Baire-category framework.Banach–Steinhaus theoremRelated: It shares the completeness-based foundation and is often grouped with this theorem.