{
  "id": "1302.1742",
  "version": "v2",
  "published": "2013-02-07T13:38:24.000Z",
  "updated": "2013-07-11T09:03:47.000Z",
  "title": "Semigroup compactifications in terms of filters",
  "authors": [
    "Tomi Alaste"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any semitopological semigroup $S$ in terms of these filters and in terms of ideals of the corresponding $m$-admissible subalgebra of $C(S)$. Furthermore, we characterize those points in any semigroup compactification of $S$ which belong either to the smallest ideal of the semigroup compactification or to the closure of this smallest ideal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-11T09:03:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semigroup compactification",
      "smallest ideal",
      "semitopological semigroup",
      "characterize closed subsemigroups",
      "admissible subalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1742A"
    }
  }
}