{
  "id": "1911.12935",
  "version": "v1",
  "published": "2019-11-29T03:26:12.000Z",
  "updated": "2019-11-29T03:26:12.000Z",
  "title": "The $G$-connected property and $G$-topological groups",
  "authors": [
    "Yongxing Wu",
    "Fucai Lin"
  ],
  "comment": "10",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "In this paper, we discuss some properties of of $G$-hull, $G$-kernel and $G$-connectedness, and extend some results of \\cite{life34}. In particular, we prove that the $G$-connectedness are preserved by countable product. Moreover, we introduce the concept of $G$-topological group, and prove that a $G$-topological group is a $G$-topology under the assumption of the regular method preserving the subsequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-29T03:26:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40J05",
      "54A05",
      "22A05"
    ],
    "keywords": [
      "topological group",
      "connected property",
      "connectedness",
      "countable product",
      "assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}