{
  "id": "2003.08843",
  "version": "v1",
  "published": "2020-03-18T05:54:14.000Z",
  "updated": "2020-03-18T05:54:14.000Z",
  "title": "Quotient with respect to admissible $L$-subgyrogroups",
  "authors": [
    "Meng Bao",
    "Fucai Lin"
  ],
  "comment": "9 pages. arXiv admin note: text overlap with arXiv:1911.12938, arXiv:2003.06132",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background of $c$-ball of relativistically admissible velocities with Einstein velocity addition. The class of topological gyrogroups is just the gyrogroups endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous, which is a good generalization of topological groups. In this paper, we are going to establish that for a locally compact admissible $L$-subgyrogroup $H$ of a strongly topological gyrogroup $G$, the natural quotient mapping $\\pi$ of $G$ onto the quotient space $G/H$ has some rather nice properties locally, such as, locally compactness, local pseudocompactness, local paracompactness, etc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T05:54:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "20N05",
      "18A32",
      "20A05",
      "20B30"
    ],
    "keywords": [
      "subgyrogroup",
      "admissible",
      "weaker algebraic structure",
      "topological gyrogroup",
      "einstein velocity addition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}