On the space \(\mathcal D(\Omega)\)

DOI10.1007/BF01226094zbMath0395.46036OpenAlexW2013026808MaRDI QIDQ1252997

Manuel Valdivia

Publication date: 1978

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01226094

zbMATH Keywords

Bornological Barrelled SpaceInductive Limit of Baire SpacesInfinite Dimensional Frechet SpaceSeparable Frechet SpaceSpace of Test Functions

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Barrelled spaces, bornological spaces (46A08) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Inductive and projective limits in functional analysis (46M40) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Tensor products in functional analysis (46M05)

Related Items (1)

(F)-spaces and strict (LF)-spaces

Cites Work

• On \(B_r\)-completeness
• On countable locally convex direct sums
• The space \(\mathcal D(\Omega)\) is not \(B_r\)-complete
• On countable strict inductive limits
• The space of distributions \(D'(\Omega)\) is not \(B_r\)-complete
• Completeness and the open mapping theorem

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