{
  "id": "math/0301293",
  "version": "v3",
  "published": "2003-01-24T23:11:16.000Z",
  "updated": "2004-09-20T14:28:03.000Z",
  "title": "On Regularly Branched Maps",
  "authors": [
    "H. Murat Tuncali",
    "Vesko Valov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $f\\colon X\\to Y$ be a perfect map between finite-dimensional metrizable spaces and $p\\geq 1$. It is shown that the space $C^*(X,\\R^p)$ of all bounded maps from $X$ into $\\R^p$ with the source limitation topology contains a dense $G_{\\delta}$-subset consisting of $f$-regularly branched maps. Here, a map $g\\colon X\\to\\R^p$ is $f$-regularly branched if, for every $n\\geq 1$, the dimension of the set $\\{z\\in Y\\times\\R^p: |(f\\times g)^{-1}(z)|\\geq n\\}$ is $\\leq n\\cdot\\big(\\dim f+\\dim Y\\big)-(n-1)\\cdot\\big(p+\\dim Y\\big)$. This is a parametric version of the Hurewicz theorem on regularly branched maps.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-09-20T14:28:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F45",
      "55M10",
      "54C65"
    ],
    "keywords": [
      "regularly branched maps",
      "source limitation topology contains",
      "perfect map",
      "finite-dimensional metrizable spaces",
      "parametric version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1293M"
    }
  }
}