{
  "id": "math/0204127",
  "version": "v1",
  "published": "2002-04-10T17:11:09.000Z",
  "updated": "2002-04-10T17:11:09.000Z",
  "title": "On the metrizability of spaces with a sharp base",
  "authors": [
    "Chris Good",
    "Robin W. Knight",
    "Abdul M. Mohamad"
  ],
  "comment": "10 pages. Reprinted from Topology and its Applications, in press, Chris Good, Robin W. Knight and Abdul M. Mohamad, On the metrizability of spaces with a sharp base",
  "journal": "Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 125--134, Topology Atlas, Toronto, 2002",
  "categories": [
    "math.GN"
  ],
  "abstract": "A base $\\mathcal{B}$ for a space $X$ is said to be sharp if, whenever $x\\in X$ and $(B_n)_{n\\in\\omega}$ is a sequence of pairwise distinct elements of $\\mathcal{B}$ each containing $x$, the collection $\\{\\bigcap_{j\\le n}B_j:n\\in\\omega\\}$ is a local base at $x$. We answer questions raised by Alleche et al. and Arhangel$'$ski\\u{\\i} et al. by showing that a pseudocompact Tychonoff space with a sharp base need not be metrizable and that the product of a space with a sharp base and $[0,1]$ need not have a sharp base. We prove various metrization theorems and provide a characterization along the lines of Ponomarev's for point countable bases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-10T17:11:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E20",
      "54E30"
    ],
    "keywords": [
      "sharp base",
      "metrizability",
      "pseudocompact tychonoff space",
      "local base",
      "point countable bases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4127G"
    }
  }
}