{
  "id": "2311.08814",
  "version": "v1",
  "published": "2023-11-15T09:33:35.000Z",
  "updated": "2023-11-15T09:33:35.000Z",
  "title": "The quotient spaces of topological groups with a $q$-point",
  "authors": [
    "Li-Hong Xie",
    "Hai-Hua Lin",
    "Piyu Li"
  ],
  "comment": "17",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we study the uniformities on the double coset spaces in topological groups. As an implication, the quotient spaces of topological groups with a $q$-point are studied. It mainly shows that: (1) Suppose that $G$ is a topological group with a $q$-point and $H$ is a closed subgroup of $G$; then the quotient space $G/H$ is an open and quasi-perfect preimage of a metrizable space; in particular, $G/H$ is an $M$-space. (2) Suppose that $G$ is a topological group with a strict $q$-point and $H$ is a closed subgroup of $G$; then the quotient space $G/H$ is an open and sequentially perfect preimage of a metrizable space. (3) Suppose that $G$ is a topological group with a strong $q$-point and $H$ is a closed subgroup of $G$; then the quotient space $G/H$ is an open and strongly sequentially perfect preimage of a metrizable space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-15T09:33:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "54H11",
      "54B15",
      "54C10",
      "54E15"
    ],
    "keywords": [
      "topological group",
      "quotient space",
      "closed subgroup",
      "metrizable space",
      "quasi-perfect preimage"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}