{
  "id": "1906.03640",
  "version": "v1",
  "published": "2019-06-09T13:37:49.000Z",
  "updated": "2019-06-09T13:37:49.000Z",
  "title": "The Frame of Nuclei of an Alexandroff Space",
  "authors": [
    "Francisco Ávila",
    "Guram Bezhanishvili",
    "Patrick Morandi",
    "Angel Zaldívar"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $\\mathcal{O}S$ be the frame of open sets of a topological space $S$, and let $N(\\mathcal{O}S)$ be the frame of nuclei of $\\mathcal{O}S$. For an Alexandroff space $S$, we prove that $N(\\mathcal{O}S)$ is spatial iff the infinite binary tree $\\mathscr T_2$ does not embed isomorphically into $(S, \\le)$, where $\\le$ is the specialization preorder of $S$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-09T13:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06D22",
      "06E15",
      "06A06",
      "06A05"
    ],
    "keywords": [
      "alexandroff space",
      "infinite binary tree",
      "open sets",
      "specialization preorder"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}