{
  "id": "2210.03648",
  "version": "v1",
  "published": "2022-09-20T03:05:25.000Z",
  "updated": "2022-09-20T03:05:25.000Z",
  "title": "Quotients with respect to strongly $L$-subgyrogroups",
  "authors": [
    "Ying-Ying Jin",
    "Li-Hong Xie"
  ],
  "comment": "10. arXiv admin note: substantial text overlap with arXiv:2003.08843 by other authors; text overlap with arXiv:2204.02079 by other authors",
  "categories": [
    "math.GN"
  ],
  "abstract": "A topological gyrogroup is a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. In this paper, we study the quotient gyrogroups in topological gyrogroups with respect to strongly $L$-subgyrogroups, and prove that let $(G, \\tau,\\oplus)$ be a topological gyrogroup and $H$ a closed strongly $L$-subgyrogroup of $G$, then the natural homomorphism $\\pi$ from a topological gyrogroup $G$ to its quotient topology on $G/H$ is an open and continuous mapping, and $G/H$ is a homogeneous $T_1$-space. We also establish that for a locally compact strongly $L$-subgyrogroup $H$ of a topological gyrogroup $G$, the natural quotient mapping $\\pi$ of $G$ onto the quotient space $G/H$ is a locally perfect mapping. This leads us to some interesting results on how properties of $G$ depend on the properties of $G/H$. Some classical results in topological groups are generalized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-20T03:05:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "22A30",
      "22A22",
      "20N05",
      "54H99"
    ],
    "keywords": [
      "topological gyrogroup",
      "subgyrogroup",
      "quotient space",
      "quotient topology",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}