Topological Vector Spaces

absolutely convex envelope absolutely convex neighbourhood algebraic Banach space barrelled space base of neighbourhoods bilinear bounded sets bounded subsets bourhood called canonical mapping Cauchy filter Chapter closed absolutely convex closed vector subspace closure compact linear mapping compact set compact subset complete space contained continuous linear form continuous linear mapping Corollary defined direct sum topology dual pair equicontinuous finer finest convex topology finite-dimensional form a base Frechet space fully complete space functions Hence inductive limit isomorphism Lemma Mackey space metrisable convex space metrisable space nearly closed neighbourhood in F normed space polar topology projective limit Proof Prop Proposition quotient seminorms separated convex space small of order space F space with dual spaces Ey strict inductive limit strong dual Suppl Suppose topological direct sum topological space topological vector space topology of convergence topology of uniform transpose uniform convergence vector subspace weakly continuous