Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov’s potential density

DOI10.1090/S0002-9939-10-10302-5zbMath1208.22001arXiv0912.0497MaRDI QIDQ3581119

Dikran Dikranjan, Dmitrij B. Shakhmatov

Publication date: 16 August 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0497

zbMATH Keywords

densityhomomorphismabelian groupprecompact groupmonomorphismpotentially dense set

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Compact groups (22C05) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Product spaces in general topology (54B10) Separability of topological spaces (54D65) Abelian groups (20K99)

Related Items

Group topologies making every continuous homomorphic image to a compact group connected ⋮ Topological groups with many small subgroups ⋮ Zariski topology and Markov topology on groups ⋮ The Markov-Zariski topology of an abelian group ⋮ A complete solution of Markov's problem on connected group topologies ⋮ Groups with cofinite Zariski topology and potential density ⋮ A Kronecker-Weyl theorem for subsets of Abelian groups. ⋮ Selectively pseudocompact groups without infinite separable pseudocompact subsets

Cites Work

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• The Markov-Zariski topology of an abelian group
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• Independent group topologies on abelian groups
• Algebraic structure of pseudocompact groups
• Weakly complete free topological groups