On the non-existence of the Mackey topology for locally quasi-convex groups

DOI10.1515/forum-2017-0179zbMath1397.22002OpenAlexW2792971126MaRDI QIDQ1791224

Lydia Außenhofer

Publication date: 4 October 2018

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum-2017-0179

zbMATH Keywords

locally quasi-convex topologyMackey topologycompatible topologyKronecker's approximation theoremGraev free abelian groupMarkov free abelian groupProtasov-Zelenyuk topologyquasi-convex hull

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Congruences; primitive roots; residue systems (11A07) Locally convex Fréchet spaces and (DF)-spaces (46A04) General properties and structure of LCA groups (22B05)

Related Items

On the existence of topologies compatible with a group duality with predetermined properties ⋮ On \(g\)-barrelled groups and their permanence properties ⋮ A locally quasi-convex abelian group without a Mackey group topology ⋮ On local quasi-convexity as a three-space property in topological abelian groups ⋮ A class of topological groups which do not admit normal compatible locally quasi-convex topologies ⋮ Locally quasi-convex compatible topologies on locally compact abelian groups ⋮ Compatible group topologies on a locally quasi-convex abelian group and the Mackey group problem ⋮ The group \(\mathbb{Z}^{( \mathbb{N})}\) does not have a Mackey topology ⋮ The Mackey problem for free locally convex spaces ⋮ The Mackey problem for free abelian topological groups ⋮ Mackey groups and Mackey topologies

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