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Some new classes of topological vector spaces with closed graph theorems. (English) Zbl 0778.46006
Summary: 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 Pták duality to the non-locally-convex situation.

MSC:
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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