{
  "id": "1401.4146",
  "version": "v1",
  "published": "2014-01-16T19:50:53.000Z",
  "updated": "2014-01-16T19:50:53.000Z",
  "title": "Independence of the metric in the fine $C^0$-topology of a function space",
  "authors": [
    "Francisco J. González Acuña"
  ],
  "comment": "This is a translation of the paper \"{\\em Independencia de la m\\'etrica en la $C^0$ topolog\\'ia fina de un espacio de funciones}\". Vol.\\ 3 (1963) pp.\\ 29-35.\\ Anales del Instituto de Matem\\'aticas (Universidad Nacional Aut\\'onoma M\\'exico). I thank Francisco Marmolejo for writing this translation. 5 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that, for any topological space $X$ and any metric space $(Y,d)$, the fine topology on the space of continuous functions from $X$ into $Y$ is independent of the metric $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-16T19:50:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function space",
      "independence",
      "metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.4146G"
    }
  }
}