Topological Vector Spaces1967 - Linear topological spaces - 406 pages |
Common terms and phrases
algebraic balanced neighborhood Banach space barrelled bornivorous bornological bounded set bounded subset canonical Cauchy filter Cauchy sequence closed subspace compact subset contains continuous linear form continuous linear map converges convex Hausdorff space convex neighborhood convex set corol Corollary defined denote direct sum dual system elements epimorphism equicontinuous subset example exerc exists a neighborhood f is continuous filter basis finer finest locally convex finite family finite subset Frechet Fréchet space fundamental system Hausdorff topology hence Hint homomorphism hyperplane infrabarrelled injection isomorphism lemma Let F locally convex Hausdorff locally convex space locally convex topology map f metric space metrizable Montel space normed vector space open set precompact Proof Proposition prove satisfies Schwartz space semi-norms space and let space F subsets of F Suppose system of neighborhoods theorem topological space topological vector space topology E,E topology induced topology on F ΕΙ