Abelian Groups which Satisfy Pontryagin Duality need not Respect Compactness

DOI10.2307/2159552zbMath0826.22002OpenAlexW4245803498MaRDI QIDQ4039325

F. Javier Trigos-Arrieta, Dieter Remus

Publication date: 20 September 1994

Full work available at URL: https://doi.org/10.2307/2159552

zbMATH Keywords

character groupPontryagin dualityadditive groupsMontel spacestopological Abelian groupreflexive infinite-dimensional real Banach spaces

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Duality theorems for locally compact groups (22D35) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

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Cites Work

• Compactness in Abelian topological groups
• Interval of group topologies satisfying Pontryagin duality
• Extensions of Pontryagin duality
• Some examples on linear topological spaces
• Über nicht-vollständige Montelräume
• Continuity, boundedness, connectedness and the Lindelöf property for topological groups
• Extensions of the Pontrjagin duality. I: Infinite products
• A group-theoretic method in approximation theory
• Extensions of the Pontrjagin duality. II: Direct and inverse sequences
• The Pontrjagin duality theorem in linear spaces
• Zur Dualitätstheorie projektiver Limites abelscher Gruppen
• Uniform Boundedness for Groups
• k-Groups and Duality
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