{
  "id": "1706.02190",
  "version": "v1",
  "published": "2017-06-07T13:54:45.000Z",
  "updated": "2017-06-07T13:54:45.000Z",
  "title": "The $k$-property and countable tightness of free topological vector spaces",
  "authors": [
    "Fucai Lin"
  ],
  "comment": "7",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "The free topological vector space $V(X)$ over a Tychonoff space $X$ is a pair consisting of a topological vector space $V(X)$ and a continuous map $i=i_{X}: X\\rightarrow V(X)$ such that every continuous mapping $f$ from $X$ to a topological vector space $E$ gives rise to a unique continuous linear operator $\\overline{f}: V(X)\\rightarrow E$ with $f=\\overline{f}\\circ i$. In this paper the $k$-property and countable tightness of free topological vector space $V(X)$ over a metrizable space $X$ are studied. For a metrizable space $X$, it is proved that the free topological vector space $V(X)$ is a $k$-space if and only if $X$ is a $k_{\\omega}$-space, and the tightness of $V(X)$ is countable if and only $X$ is separable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-07T13:54:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "46A05",
      "54A25",
      "54D50"
    ],
    "keywords": [
      "free topological vector space",
      "countable tightness",
      "unique continuous linear operator",
      "metrizable space",
      "continuous map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}