{
  "id": "1412.4393",
  "version": "v1",
  "published": "2014-12-14T18:38:08.000Z",
  "updated": "2014-12-14T18:38:08.000Z",
  "title": "Discretization of topological spaces",
  "authors": [
    "Massoud Amini",
    "Nasser Golestani"
  ],
  "comment": "19 pages",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compactification functor. The interpretations of discretization in the level of algebras of functions are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-14T18:38:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35",
      "46L85",
      "46M15"
    ],
    "keywords": [
      "topological spaces",
      "compactification functor",
      "standard discretization",
      "original topology",
      "compactification procedures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4393A"
    }
  }
}