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Quasi totally barrelled spaces. (English) Zbl 0745.46004

Summary: We introduce the new class of quasi totally barrelled locally convex spaces which is more general than the totally barrelled one. Examples which separate this class from anothers are given. We study its hereditary properties and we give a closed-graph theorem for them. We also extend our study to the general case of topological vector spaces.

MSC:

46A08 Barrelled spaces, bornological spaces
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
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