Characterized Subgroups of Topological Abelian Groups

Axioms

Dikran Dikranjan¹  Daniele Impieri¹  Anna Giordano Bruno¹ 

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Via delle Scienze 206, Udine 33100, Italy;

关键词: characterized subgroup;    T-characterized subgroup;    T-sequence;    TB-sequence;    von Neumann radical;    convergent sequence;    null sequence;    abelian group;   

DOI  :  10.3390/axioms4040459

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown