{
  "id": "math/0302239",
  "version": "v1",
  "published": "2003-02-19T18:54:16.000Z",
  "updated": "2003-02-19T18:54:16.000Z",
  "title": "Limits in Function Spaces and Compact Groups",
  "authors": [
    "Joan E. Hart",
    "Kenneth Kunen"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "If B is an infinite subset of omega and X is a topological group, let C^X_B be the set of all x in X such that <x^n : n in B> converges to 1. If F is a filter of infinite sets, let D^X_F be the union of all the C^X_B for B in F. The C^X_B and D^X_F are subgroups of X when X is abelian. In the circle group T, it is known that C^X_B always has measure 0. We show that there is a filter F such that D^T_F has measure 0 but is not contained in any C^X_B. There is another filter G such that D^X_G = T. We also describe the relationship between D^T_F and the D^X_F for arbitrary compact groups X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-19T18:54:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "22C05"
    ],
    "keywords": [
      "function spaces",
      "arbitrary compact groups",
      "infinite subset",
      "infinite sets",
      "circle group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2239H"
    }
  }
}