{
  "id": "1407.0503",
  "version": "v1",
  "published": "2014-07-02T09:58:52.000Z",
  "updated": "2014-07-02T09:58:52.000Z",
  "title": "Extension of continuous mappings and $H_1$-retracts",
  "authors": [
    "Olena Karlova"
  ],
  "journal": "Bull. Aust. Math. Soc., Volume 78, Issue 03, 2008, P. 497-506",
  "doi": "10.1017/S0004972708000907",
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that any continuous mapping $f:E\\to Y$ on a completely metrizable subspace $E$ of a perfect paracompact space $X$ can be extended to a Lebesgue class one mapping $g:X\\to Y$ (i.e. for every open set $V$ in $Y$ the preimage $g^{-1}(V)$ is an $F_\\sigma$-set in $X$) with values in an arbitrary topological space $Y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-02T09:58:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C20",
      "54C05"
    ],
    "keywords": [
      "continuous mapping",
      "perfect paracompact space",
      "open set",
      "lebesgue class",
      "arbitrary topological space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0503K"
    }
  }
}