{
  "id": "2104.11877",
  "version": "v1",
  "published": "2021-04-24T03:50:21.000Z",
  "updated": "2021-04-24T03:50:21.000Z",
  "title": "A class of quotient spaces in strongly topological gyrogroups",
  "authors": [
    "Meng Bao",
    "Jie Wang",
    "Xiaoquan Xu"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:2003.06132, arXiv:2103.11566, arXiv:1911.12938, arXiv:2003.08843, arXiv:2011.02633, arXiv:2102.05860",
  "categories": [
    "math.GN"
  ],
  "abstract": "Quotient space is a class of the most important topological spaces in the research of topology. In this paper, we show that if G is a strongly topological gyrogroup with a symmetric neighborhood base U at 0 and H is an admissible subgyrogroup generated from U , then G/H is first-countable if and only if it is metrizable. Moreover, if H is neutral and G/H is Frechet-Urysohn with an {\\omega}{\\omega}-base, then G/H is first-countable. Therefore, we obtain that if H is neutral, then G/H is metrizable if and only if G/H is Frechet-Urysohn with an {\\omega}{\\omega}-base. Finally, it is shown that if H is neutral, {\\pi}\\c{hi}(G/H) = \\c{hi}(G/H) and {\\pi}{\\omega}(G/H) = {\\omega}(G/H).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-24T03:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "11B05",
      "26A03",
      "40A05",
      "40A30",
      "40A99"
    ],
    "keywords": [
      "strongly topological gyrogroup",
      "quotient space",
      "symmetric neighborhood base",
      "frechet-urysohn",
      "important topological spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}