Characterized Subgroups of Topological Abelian Groups
Copyright policy )Characterized Subgroups of Topological Abelian Groups
A subgroup H of a topological abelian group X is said to be characterized by a sequence v = (vn) of characters of X if H = {x ∈ X : vn(x) → 0 in T}. We study the basic properties of characterized subgroups in the general setting, extending results known in the compact case. For a better description, we isolate various types of characterized subgroups. Moreover, we introduce the relevant class of auto-characterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally compact abelian groups, these are proven to be exactly the non-compact ones. As a by-product of our results, we find a complete description of the characterized subgroups of discrete abelian groups.
- University of Udine Italy
Group Theory (math.GR), QA1-939, FOS: Mathematics, <em>T</em>-sequence, von Neumann radical, <em>T</em>-characterized subgroup, Mathematics - General Topology, \(T\)-characterized subgroup, null sequence, T-characterized subgroup, characterized subgroup; T-characterized subgroup; T-sequence; TB-sequence; von Neumann radical; convergent sequence; null sequence; abelian group., General Topology (math.GN), General properties and structure of LCA groups, abelian group, characterized subgroup, <em>TB</em>-sequence, T-sequence, Analysis on general topological groups, \(T\)-sequence, 22A10, 43A40, 54H11, 22B05, 20K45, convergent sequence, Topological methods for abelian groups, \(TB\)-sequence, Character groups and dual objects, Mathematics - Group Theory, Mathematics, TB-sequence, Topological groups (topological aspects)
Group Theory (math.GR), QA1-939, FOS: Mathematics, <em>T</em>-sequence, von Neumann radical, <em>T</em>-characterized subgroup, Mathematics - General Topology, \(T\)-characterized subgroup, null sequence, T-characterized subgroup, characterized subgroup; T-characterized subgroup; T-sequence; TB-sequence; von Neumann radical; convergent sequence; null sequence; abelian group., General Topology (math.GN), General properties and structure of LCA groups, abelian group, characterized subgroup, <em>TB</em>-sequence, T-sequence, Analysis on general topological groups, \(T\)-sequence, 22A10, 43A40, 54H11, 22B05, 20K45, convergent sequence, Topological methods for abelian groups, \(TB\)-sequence, Character groups and dual objects, Mathematics - Group Theory, Mathematics, TB-sequence, Topological groups (topological aspects)
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