{
  "id": "math/0412447",
  "version": "v2",
  "published": "2004-12-22T11:35:00.000Z",
  "updated": "2005-01-28T15:33:41.000Z",
  "title": "Sequences and filters of characters characterizing subgroups of compact abelian groups",
  "authors": [
    "Mathias Beiglböck",
    "Christian Steineder",
    "Reinhard Winkler"
  ],
  "comment": "laTex2e, 10 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let H be a countable subgroup of the metrizable compact abelian group G and f:H -> T=R/Z a (not necessarily continuous) character of H. Then there exists a sequence (chi_n)_n of (continuous) characters of G such that lim_n chi_n(alpha) = f(alpha) for all alpha in H and (chi_n(alpha))_n does not converge whenever alpha in G\\H. If one drops the countability and metrizability requirement one can obtain similar results by using filters of characters instead of sequences. Furthermore the introduced methods allow to answer questions of Dikranjan et al.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-28T15:33:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22C05",
      "54H11"
    ],
    "keywords": [
      "characters characterizing subgroups",
      "metrizable compact abelian group",
      "metrizability requirement",
      "similar results"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12447B"
    }
  }
}