{
  "id": "math/0004135",
  "version": "v1",
  "published": "2000-04-20T20:09:45.000Z",
  "updated": "2000-04-20T20:09:45.000Z",
  "title": "A note on a question of R. Pol concerning light maps",
  "authors": [
    "V. V. Uspenskij"
  ],
  "comment": "4 pages. Topology Appl. (to appear)",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let f:X -> Y be an onto map between compact spaces such that all point-inverses of f are zero-dimensional. Let A be the set of all functions u:X -> I=[0,1] such that $u[f^\\leftarrow(y)]$ is zero-dimensional for all y in Y. Do almost all maps u:X -> I, in the sense of Baire category, belong to A? H. Toru\\'nczyk proved that the answer is yes if Y is countable-dimensional. We extend this result to the case when Y has property C.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-04-20T20:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C10",
      "54C35",
      "54E52",
      "54F45"
    ],
    "keywords": [
      "pol concerning light maps",
      "baire category",
      "compact spaces",
      "zero-dimensional",
      "point-inverses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......4135U"
    }
  }
}