Metrizability of precompact subsets in (LF)-spaces

DOI10.1017/S0308210500018941zbMath0622.46005OpenAlexW2096797496MaRDI QIDQ3759349

José Orihuela, Bernardo Cascales

Publication date: 1986

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500018941

zbMATH Keywords

metrizability(LF)-spaceprecompactquasi-Suslin spacedual metric spacessequentially retractiveevery (LF)-space is angelicmetrizable completionprecompactly retractiveregularity and retractivity problems for the weak topologiesregularity in inductive limitssequentially compact-regular

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Inductive and projective limits in functional analysis (46M40) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items

Weight of precompact subsets and tightness ⋮ On compactness in locally convex spaces ⋮ Bornological spaces of null sequences ⋮ On \(s\)-barrelled spaces ⋮ On bounded sets in \(C_k ( X )\) ⋮ Real analytic parameter dependence of solutions of differential equations ⋮ On metrizability of compactoid sets in non-archimedean locally convex spaces ⋮ Necessary and sufficient conditions for precompact sets to be metrisable ⋮ On K-analytic locally convex spaces ⋮ Null Sequences in Coechelon Spaces

Cites Work

• Über die Regularitätsbegriffe induktiver lokalkonvexer Sequenzen
• Bemerkungen über die Approximationseigenschaft lokalkonvexer Funktionenräume. (Remarks on the approximation property of locally convex function spaces)
• Folgenretraktive Sequenzen lokalkonvexer Räume.