Abstract:In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pt\'ak duality to the non-locally-convex situation.
Keywords: inverse seminorm, Mackey seminorm, nearly-semi-continuous, semi-barrelled, semi-$B$-complete, semi-infra-(s), semi-Mackey
AMS Subject Classification: 46A30, 47A05