{
  "id": "1101.4400",
  "version": "v1",
  "published": "2011-01-23T18:45:06.000Z",
  "updated": "2011-01-23T18:45:06.000Z",
  "title": "Another approach to parametric Bing and Krasinkiewicz maps",
  "authors": [
    "Vesko Valov"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Using a factorization theorem due to Pasynkov we provide a short proof of the existence and density of parametric Bing and Krasinkiewicz maps. In particular, the following corollary is established: Let $f\\colon X\\to Y$ be a surjective map between paracompact spaces such that all fibers $f^{-1}(y)$, $y\\in Y$, are compact and there exists a map $g\\colon X\\to\\mathbb I^{\\aleph_0}$ embedding each $f^{-1}(y)$ into $\\mathbb I^{\\aleph_0}$. Then for every $n\\geq 1$ the space $C^*(X,\\mathbb R^n)$ of all bounded continuous functions with the uniform convergence topology contains a dense set of maps $g$ such that any restriction $g|f^{-1}(y)$, $y\\in Y$, is a Bing and Krasinkiewicz map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-23T18:45:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E40",
      "54F15"
    ],
    "keywords": [
      "krasinkiewicz map",
      "parametric bing",
      "uniform convergence topology contains",
      "factorization theorem",
      "short proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}