{
  "id": "1512.07515",
  "version": "v1",
  "published": "2015-12-23T15:28:41.000Z",
  "updated": "2015-12-23T15:28:41.000Z",
  "title": "Countable tightness and $\\mathfrak G$-bases on Free topological groups",
  "authors": [
    "Fucai Lin",
    "Alex Ravsky",
    "Jing Zhang"
  ],
  "comment": "11. arXiv admin note: text overlap with arXiv:1507.04912",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we discuss two topological properties in $F(X)$ or $A(X)$, namely the countable tightness and $\\mathfrak G$-base. We provide some characterizations of the countable tightness and $\\mathfrak G$-base of $F(X)$ and $A(X)$ for various special classes of spaces $X$. Furthermore, we also study the countable tightness and $\\mathfrak G$-base of some level of $F(X)$. Some open problems in \\cite{GKL} are partially answered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-23T15:28:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "22A05",
      "54E20",
      "54E35",
      "54D50",
      "54D55"
    ],
    "keywords": [
      "free topological group",
      "countable tightness",
      "free abelian topological group",
      "tychonoff space",
      "special classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151207515L"
    }
  }
}