A Kronecker-Weyl theorem for subsets of Abelian groups.

DOI10.1016/j.aim.2010.12.016zbMath1266.20063arXiv1012.4177OpenAlexW2070499093MaRDI QIDQ633594

Dikran Dikranjan, Dmitrij B. Shakhmatov

Publication date: 29 March 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4177

zbMATH Keywords

Zariski closuresMarkov problemDiophantine approximationBohr topologyZariski topologyuniform distributionmonomorphismsBohr compactificationBaire propertyWeyl criterionalmost torsion setsdiscrete flowspotentially dense setstopological Abelian groups

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Descriptive set theory (03E15) Baire category, Baire spaces (54E52) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Well-distributed sequences and other variations (11K36) Diophantine approximation in probabilistic number theory (11K60) Topological methods for abelian groups (20K45)

Related Items

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 ⋮ Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov’s potential density ⋮ Selectively pseudocompact groups without infinite separable pseudocompact subsets ⋮ The impact of the Bohr topology on selective pseudocompactness

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