Solutions of D. A. Raikov's problems in the theory of topological vector spaces

DOI10.1134/S1061920808040092zbMath1190.46002MaRDI QIDQ1033808

O. G. Smolyanov

Publication date: 10 November 2009

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

nonclosed sequentially closed subsetspaces \(\mathcal D\) and \(\mathcal D'\)

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) General theory of locally convex spaces (46A03) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30)

Cites Work

• Hypercomplete linear topological spaces
• Theorems and problems in functional analysis. Transl. from the Russian by Harold H. McFaden
• On \(B_r\)-completeness
• Sequentially closed subsets of products of locally convex spaces
• The space of distributions \(D'(\Omega)\) is not \(B_r\)-complete
• La dualité dans les espaces \((\mathcal F)\) et \((\mathcal{LF})\)
• Sur certains espaces vectoriels topologiques
• Gateaux complex differentiability and continuity
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