KnowraHahn–Banach theoremLinked fromLinked fromThe 13 pages that link to Hahn–Banach theorem, each with the reason it gives.All 13Broader topic 2Related 8Compared with 3Axiom of choiceRelated: Standard proofs use choice principles to extend functionals across arbitrary spaces.Dual spaceRelated: It ensures continuous duals contain enough functionals to separate points and support.Functional analysisRelated: It guarantees that functionals can separate points and extend across spaces.Riesz representation theoremCompared with: It applies broadly to normed spaces, while Riesz representation requires Hilbert-space structure.Weak topologyRelated: Its separation results show how continuous linear functionals distinguish points and convex sets.Stefan BanachBroader topic: It supplies a foundational extension principle in the functional analysis Banach helped build.Uniform boundedness principleRelated: Together, these theorems provide foundational tools for reasoning about bounded linear functionals.Riesz–Markov–Kakutani representation theoremCompared with: Hahn–Banach guarantees extensions, while this theorem identifies functionals through measures.Existence theoremBroader topic: It guarantees the existence of extensions that support results throughout functional analysis.Fenchel–Moreau theoremRelated: Its separation form underpins the affine separation used in the proof.Hyperplane separation theoremRelated: Separation theorems in topological vector spaces follow from Hahn–Banach extension.Banach–Mazur theoremRelated: It provides functionals that detect vector norms, enabling an isometric representation.Lions–Lax–Milgram theoremCompared with: It is a foundational functional-analysis result, but does not itself give variational solvability.