{
  "id": "math/0609092",
  "version": "v1",
  "published": "2006-09-04T07:19:09.000Z",
  "updated": "2006-09-04T07:19:09.000Z",
  "title": "Resolvability and monotone normality",
  "authors": [
    "Istvan Juhasz",
    "Lajos Soukup",
    "Zoltan Szentmiklossy"
  ],
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "A space $X$ is said to be $\\kappa$-resolvable (resp. almost $\\kappa$-resolvable) if it contains $\\kappa$ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). $X$ is maximally resolvable iff it is $\\Delta(X)$-resolvable, where $\\Delta(X) = \\min\\{|G| : G \\ne \\emptyset {open}\\}.$ We show that every crowded monotonically normal (in short: MN) space is $\\omega$-resolvable and almost $\\mu$-resolvable, where $\\mu = \\min\\{2^{\\omega}, \\omega_2 \\}$. On the other hand, if $\\kappa$ is a measurable cardinal then there is a MN space $X$ with $\\Delta(X) = \\kappa$ such that no subspace of $X$ is $\\omega_1$-resolvable. Any MN space of cardinality $< \\aleph_\\omega$ is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space $X$ with $|X| = \\Delta(X) = \\aleph_{\\omega}$ such that no subspace of $X$ is $\\omega_2$-resolvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-04T07:19:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A35",
      "03E35",
      "54A25"
    ],
    "keywords": [
      "monotone normality",
      "resolvable",
      "mn space",
      "resolvability",
      "supercompact cardinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9092J"
    }
  }
}