{
  "id": "1311.1719",
  "version": "v1",
  "published": "2013-11-07T15:51:44.000Z",
  "updated": "2013-11-07T15:51:44.000Z",
  "title": "Regular spaces of small extent are omega-resolvable",
  "authors": [
    "Istvan Juhasz",
    "Lajos Soukup",
    "Zoltan Szentmiklossy"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the smallest size of a non-empty open set in X and ext(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindel\\\"of spaces of uncountable dispersion character are omega-resolvable. We also prove that any regular Lindel\\\"of space X with |X|=\\Delta(X)=omega_1 is even omega_1-resolvable. The question if regular Lindel\\\"of spaces of uncountable dispersion character are maximally resolvable remains wide open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-07T15:51:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A35",
      "03E35",
      "54A25"
    ],
    "keywords": [
      "regular space",
      "small extent",
      "uncountable dispersion character",
      "omega-resolvable",
      "maximally resolvable remains wide open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1719J"
    }
  }
}