{
  "id": "0802.4436",
  "version": "v2",
  "published": "2008-02-29T17:31:24.000Z",
  "updated": "2008-03-28T03:42:59.000Z",
  "title": "Krasinkiewicz spaces and parametric Krasinkiewicz maps",
  "authors": [
    "Eiichi Matsuhashi",
    "Vesko Valov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GN",
    "math.GT"
  ],
  "abstract": "We say that a metrizable space $M$ is a Krasinkiewicz space if any map from a metrizable compactum $X$ into $M$ can be approximated by Krasinkiewicz maps (a map $g\\colon X\\to M$ is Krasinkiewicz provided every continuum in $X$ is either contained in a fiber of $g$ or contains a component of a fiber of $g$). In this paper we establish the following property of Krasinkiewicz spaces: Let $f\\colon X\\to Y$ be a perfect map between metrizable spaces and $M$ a Krasinkiewicz complete $ANR$-space. If $Y$ is a countable union of closed finite-dimensional subsets, then the function space $C(X,M)$ with the source limitation topology contains a dense $G_{\\delta}$-subset of maps $g$ such that all restrictions $g|f^{-1}(y)$, $y\\in Y$, are Krasinkiewicz maps. The same conclusion remains true if $M$ is homeomorphic to a closed convex subset of a Banach space and $X$ is a $C$-space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-28T03:42:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F15",
      "54F45",
      "54E40"
    ],
    "keywords": [
      "parametric krasinkiewicz maps",
      "krasinkiewicz space",
      "source limitation topology contains",
      "metrizable space",
      "conclusion remains true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.4436M"
    }
  }
}