{\displaystyle f_{i}:Y\to \mathbb {K} } is a continuous linear functional. By the Hahn–Banach theorem, we may extend each f i {\displaystyle f_{i}} to a continuous...

the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has...

proofs of versions of the open mapping theorem, closed graph theorem, and Hahn–Banach theorem. Grothendieck, Alexander (1955). "Produits Tensoriels Topologiques...