{
  "id": "1606.01967",
  "version": "v1",
  "published": "2016-06-06T22:37:58.000Z",
  "updated": "2016-06-06T22:37:58.000Z",
  "title": "$\\mathfrak G$-bases in free (locally convex) topological vector spaces",
  "authors": [
    "Taras Banakh",
    "Arkady Leiderman"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GN",
    "math.FA",
    "math.LO"
  ],
  "abstract": "We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\\mathfrak G$-base. A topological space $X$ has a local $\\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_\\alpha)_{\\alpha\\in\\omega^\\omega}$ such that $U_\\beta\\subset U_\\alpha$ for all $\\alpha\\le\\beta$ in $\\omega^\\omega$. To construct $\\mathfrak G$-bases in free topological vector spaces, we exploit a new description of the topology of a free topological vector space over a topological (or more generally, uniform) space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-06T22:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D70",
      "54D45",
      "46A03",
      "06A06",
      "54A35",
      "54C30",
      "54E15",
      "54E20",
      "54E35"
    ],
    "keywords": [
      "locally convex",
      "free topological vector space",
      "neighborhood base",
      "topological space",
      "description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}