{
  "id": "0803.1175",
  "version": "v1",
  "published": "2008-03-07T20:42:52.000Z",
  "updated": "2008-03-07T20:42:52.000Z",
  "title": "Pre-Hausdorff Spaces",
  "authors": [
    "Jay Stine",
    "M. V. Mielke"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "This paper introduces three separation conditions for topological spaces, called T_{0,1}, T_{0,2} (\"pre-Hausdorff\"), and T_{1,2}. These conditions generalize the classical T_(1) and T_(2) separation axioms, and they have advantages over them topologically which we discuss. We establish several different characterizations of pre-Hausdorff spaces, and a characterization of Hausdorff spaces in terms of pre-Hausdorff. We also discuss some classical Theorems of general topology which can or cannot be generalized by replacing the Hausdorff condition by pre-Hausdorff.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-07T20:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18B30",
      "54A05",
      "54D10"
    ],
    "keywords": [
      "pre-hausdorff spaces",
      "hausdorff condition",
      "separation axioms",
      "general topology",
      "separation conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1175S"
    }
  }
}