Linear topologies on \(\mathbb Z\) are not Mackey topologies

DOI10.1016/J.JPAA.2012.01.005zbMath1255.22001arXiv1107.2661OpenAlexW2963300475MaRDI QIDQ456821

Daniel de la Barrera Mayoral, Lydia Außenhofer

Publication date: 16 October 2012

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.2661

zbMATH Keywords

locally quasi-convex topologyMackey topology\(p\)-adic topologylinear topology

Mathematics Subject Classification ID

Representations of general topological groups and semigroups (22A25) Topological groups (topological aspects) (54H11) (p)-adic theory, local fields (11F85) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (15)

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks ⋮ Locally quasi-convex compatible topologies on a topological group ⋮ The Mackey topology problem: a complete solution for bounded groups ⋮ On local quasi-convexity as a three-space property in topological abelian groups ⋮ Locally quasi-convex compatible topologies on locally compact abelian groups ⋮ Report on the open problems session ⋮ Non metrizable topologies on Z with countable dual group. ⋮ The group \(\mathbb{Z}^{( \mathbb{N})}\) does not have a Mackey topology ⋮ \(\mathbb{Q}\) is not a Mackey group ⋮ ``Varopoulos paradigm: Mackey property versus metrizability in topological groups ⋮ Characterizing sequences for precompact group topologies ⋮ On the non-existence of the Mackey topology for locally quasi-convex groups ⋮ Factorizable subgroups of the circle group ⋮ Characteristics of the Mackey Topology for Abelian Topological Groups ⋮ Mackey groups and Mackey topologies

Cites Work

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• Groups of quasi-invariance and the Pontryagin duality
• Locally compact abelian groups admitting non-trivial quasi-convex null sequences
• Topological groups and related structures
• Countably infinite quasi-convex sets in some locally compact abelian groups
• Quasi-convex sequences in the circle and the 3-adic integers
• Answer to Raczkowski's questions on convergent sequences of integers
• A Mackey-Arens theorem for topological Abelian groups
• Locally quasi-convex compatible topologies on a topological group
• TOPOLOGIES ON ABELIAN GROUPS

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