{
  "id": "math/0209074",
  "version": "v1",
  "published": "2002-09-06T20:56:07.000Z",
  "updated": "2002-09-06T20:56:07.000Z",
  "title": "On finite-dimensional maps",
  "authors": [
    "H. Murat Tuncali",
    "Vesko Valov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $f\\colon X\\to Y$ be a perfect surjective map of metrizable spaces. It is shown that if $Y$ is a $C$-space (resp., $\\dim Y\\leq n$ and $\\dim f\\leq m$), then the function space $C(X,\\uin^{\\infty})$ (resp., $C(X,\\uin^{2n+1+m})$) equipped with the source limitation topology contains a dense $G_{\\delta}$-set $\\mathcal{H}$ such that $f\\times g$ embeds $X$ into $Y\\times\\uin^{\\infty}$ (resp., into $Y\\times\\uin^{2n+1+m}$) for every $g\\in\\mathcal{H}$. Some applications of this result are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-06T20:56:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F45",
      "55M10"
    ],
    "keywords": [
      "finite-dimensional maps",
      "source limitation topology contains",
      "function space",
      "perfect surjective map",
      "metrizable spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9074M"
    }
  }
}