{
  "id": "math/0301085",
  "version": "v7",
  "published": "2003-01-09T15:28:35.000Z",
  "updated": "2010-10-31T19:04:55.000Z",
  "title": "The Hurewicz covering property and slaloms in the Baire space",
  "authors": [
    "Boaz Tsaban"
  ],
  "comment": "Small updates",
  "journal": "Fundamenta Mathematicae 181 (2004), 273--280",
  "doi": "10.4064/fm181-3-5",
  "categories": [
    "math.GN",
    "math.CO",
    "math.LO"
  ],
  "abstract": "According to a result of Kocinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals $X$ satisfies the Hurewicz property if, and only if, each large open cover of $X$ contains a groupable subcover. This solves in the affirmative a problem of Scheepers. The proof uses a rigorously justified abuse of notation and a \"structure\" counterpart of a combinatorial characterization, in terms of slaloms, of the minimal cardinality b of an unbounded family of functions in the Baire space. In particular, we obtain a new characterization of $\\b$.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2010-10-31T19:04:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "26A03",
      "03E75"
    ],
    "keywords": [
      "hurewicz covering property",
      "baire space",
      "large open cover",
      "somewhat simpler selection property",
      "characterization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1085T"
    }
  }
}