Topological Vector Spaces

arbitrary Archimedean balanced neighborhood Banach space barreled barreled space bornological space bounded set bounded subset called complete vector lattice continuous linear convergence convex and balanced COROLLARY DEFINITION directed vector space easily verified finite follows G₁ Hausdorff locally convex hence implies isomorphic lemma let us assume Let us denote linear functional locally convex lattice locally convex space locally convex topology locally full topology locally solid topology Math Minkowski functional n}nen neighborhood basis normal subspace normed lattice normed vector space obviously ordered vector space origin positive elements product topology proof is complete quasinorm Remark Section sequence of elements sequence x}EN solid seminorm space and let t)-continuous t)-neighborhood t₁ theorem topological vector lattice topological vector space topology defined topology of o)-boundedness totally bounded U₁ V₁ vector subspace vector topology W₁ weakly x₁ y₁ ΔΕΔ ΜΕΝ