| Autor: |
Dikran Dikranjan, Anna Giordano Bruno, Daniele Impieri |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Axioms, Vol 4, Iss 4, Pp 459-491 (2015) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms4040459 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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