{
  "id": "2104.11875",
  "version": "v1",
  "published": "2021-04-24T03:40:52.000Z",
  "updated": "2021-04-24T03:40:52.000Z",
  "title": "Topological gyrogroups with Frechet-Urysohn property and omega^{omega}-base",
  "authors": [
    "Meng Bao",
    "Xiaoyuan Zhang",
    "Xiaoquan Xu"
  ],
  "comment": "10 pages",
  "doi": "10.1007/s41980-021-00576-w",
  "categories": [
    "math.GN"
  ],
  "abstract": "The concept of topological gyrogroups is a generalization of a topological group. In this work, ones prove that a topological gyrogroup G is metrizable iff G has an {\\omega}{\\omega}-base and G is Frechet-Urysohn. Moreover, in topological gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn and having an {\\omega}{\\omega}-base are all weakly three-space properties with H a closed L-subgyrogroup",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-24T03:40:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "11B05",
      "26A03",
      "40A05",
      "40A30",
      "40A99"
    ],
    "keywords": [
      "topological gyrogroup",
      "frechet-urysohn property",
      "compact subset",
      "weakly three-space properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}