{
  "id": "1509.01108",
  "version": "v1",
  "published": "2015-09-03T14:43:34.000Z",
  "updated": "2015-09-03T14:43:34.000Z",
  "title": "Characterized subgroups of topological abelian groups",
  "authors": [
    "Dikran Dikranjan",
    "Anna Giordano Bruno",
    "Daniele Impieri"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "A subgroup $H$ of a topological abelian group $X$ is said to be characterized by a sequence $\\mathbf v =(v_n)$ of characters of $X$ if $H=\\{x\\in X:v_n(x)\\to 0\\ \\text{in}\\ \\mathbb T\\}$. 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 autochacaracterized 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 proved 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-03T14:43:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A10",
      "43A40",
      "54H11",
      "22B05",
      "20K45"
    ],
    "keywords": [
      "characterized subgroups",
      "topological abelian group",
      "discrete abelian groups",
      "locally compact abelian groups",
      "basic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901108D"
    }
  }
}