{
  "id": "0903.0813",
  "version": "v2",
  "published": "2009-03-04T16:50:43.000Z",
  "updated": "2009-03-04T21:47:28.000Z",
  "title": "The Suslinian number and other cardinal invariants of continua",
  "authors": [
    "T. Banakh",
    "V. V. Fedorchuk",
    "J. Nikiel",
    "M. Tuncali"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "By the {\\em Suslinian number} $\\Sln(X)$ of a continuum $X$ we understand the smallest cardinal number $\\kappa$ such that $X$ contains no disjoint family $\\C$ of non-degenerate subcontinua of size $|\\C|\\ge\\kappa$. For a compact space $X$, $\\Sln(X)$ is the smallest Suslinian number of a continuum which contains a homeomorphic copy of $X$. Our principal result asserts that each compact space $X$ has weight $\\le\\Sln(X)^+$ and is the limit of an inverse well-ordered spectrum of length $\\le \\Sln(X)^+$, consisting of compacta with weight $\\le\\Sln(X)$ and monotone bonding maps. Moreover, $w(X)\\le\\Sln(X)$ if no $\\Sln(X)^+$-Suslin tree exists. This implies that under the Suslin Hypothesis all Suslinian continua are metrizable, which answers a question of \\cite{DNTTT1}. On the other hand, the negation of the Suslin Hypothesis is equivalent to the existence of a hereditarily separable non-metrizable Suslinian continuum. If $X$ is a continuum with $\\Sln(X)<2^{\\aleph_0}$, then $X$ is 1-dimensional, has rim-weight $\\le\\Sln(X)$ and weight $w(X)\\ge\\Sln(X)$. Our main tool is the inequality $w(X)\\le\\Sln(X)\\cdot w(f(X))$ holding for any light map $f:X\\to Y$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-04T21:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F15"
    ],
    "keywords": [
      "cardinal invariants",
      "separable non-metrizable suslinian continuum",
      "compact space",
      "suslin hypothesis",
      "principal result asserts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0813B"
    }
  }
}