{
  "id": "1504.01626",
  "version": "v1",
  "published": "2015-04-07T14:47:01.000Z",
  "updated": "2015-04-07T14:47:01.000Z",
  "title": "Menger remainders of topological groups",
  "authors": [
    "Angelo Bella",
    "Seçil Tokgöz",
    "Lyubomyr Zdomskyy"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it it is $\\sigma$-compact. Also, the existence of a Scheepers non-$\\sigma$-compact remainder of a topological group follows from CH and yields a $P$-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel'skii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-07T14:47:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E75",
      "54D40",
      "54D20",
      "03E35",
      "54D30",
      "54D80"
    ],
    "keywords": [
      "topological group",
      "menger remainders",
      "constrains combinatorial covering properties",
      "hurewicz impose",
      "compact remainder"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401626B"
    }
  }
}