Topological Vector Spaces: The Theory Without Convexity Conditions

6-locally 7-topological absolutely convex absolutely convex set absorbing sequence ADASCH Algebraic Assume B-complete B₂ barrelled space base of neighbourhoods bornivorous string bornological spaces bounded sets closed graph theorem closed in E(7 closed linear mapping closed string compact sets consider continuous linear mappings continuous mapping countable denote Edité Edited Ex 7x F)-space finest linear topology finite subset following proposition fundamental sequence Hausdorff linear topology hence inductive limit infra-s-space knots KÖTHE L-barrelled Let E(7 locally convex space locally topological spaces mappings from E(7 metrizable metrizable t.v.s. nearly continuous open mapping theorem pointwise bounded pological Proceedings 1974 Proof prove quotient space resp s-space Séminaire sequence of bounded sequence of compact set of strings sets in E(7 string in E(7 Theory topo topological direct sum topological in E(7 topological vector spaces topology induced U₁ U₂ Un+1 V₁ weakly singular αει αετ Μετ