{
  "id": "1805.07028",
  "version": "v1",
  "published": "2018-05-18T02:52:52.000Z",
  "updated": "2018-05-18T02:52:52.000Z",
  "title": "Free locally convex spaces and the Ascoli property",
  "authors": [
    "Saak Gabriyelyan"
  ],
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "T. Banakh showed in [2] that if $X$ is a Dieudonn\\'{e} complete space, then the free locally convex space $L(X)$ on $X$ is an Ascoli space if and only if $X$ is a countable discrete space. We give an independent, short and clearer proof of Banakh's result and remove the condition of being a Dieudonn\\'{e} complete space. Thus we have the following result: the free locally convex space $L(X)$ over a Tychonoff space $X$ is an Ascoli space if and only if $X$ is a countable discrete space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-18T02:52:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A03",
      "54D50",
      "22A05",
      "54A25"
    ],
    "keywords": [
      "free locally convex space",
      "ascoli property",
      "countable discrete space",
      "complete space",
      "ascoli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}