Characterizing subgroups of compact abelian groups
Copyright policy )Characterizing subgroups of compact abelian groups
We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter.
12 pages
- University of Wisconsin–Stevens Point United States
- UNIVERSITY OF WISCONSIN-MADISON United States
- University of Wisconsin–Madison United States
- University of Wisconsin–Oshkosh United States
- University of Udine Italy
Algebra and Number Theory, characterizing sequence, General Topology (math.GN), Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), compact abelian group, Galois correspondences, closure operators (in relation to ordered sets), g-closed subgroup, Compact groups, 54H11, characterizing set, FOS: Mathematics, characterizable subgroup, Distribution modulo one, countable subgroup, Topological groups (topological aspects), Mathematics - General Topology
Algebra and Number Theory, characterizing sequence, General Topology (math.GN), Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), compact abelian group, Galois correspondences, closure operators (in relation to ordered sets), g-closed subgroup, Compact groups, 54H11, characterizing set, FOS: Mathematics, characterizable subgroup, Distribution modulo one, countable subgroup, Topological groups (topological aspects), Mathematics - General Topology
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