{
  "id": "1710.06855",
  "version": "v1",
  "published": "2017-10-18T17:52:43.000Z",
  "updated": "2017-10-18T17:52:43.000Z",
  "title": "On Properties of Nests: Some Answers and Questions",
  "authors": [
    "Kyriakos Papadopoulos"
  ],
  "comment": "This paper has been published in the journal: Q & A in General Topology (Vol. 33, No 2, 2015.). arXiv admin note: substantial text overlap with arXiv:1302.2519",
  "journal": "Questions and Answers in General Topology, Volume 33, Number 2, 2015",
  "categories": [
    "math.GN"
  ],
  "abstract": "By considering nests on a given space, we explore order-theoretical and topological properties that are closely related to the structure of a nest. In particular, we see how subbases given by two dual nests can be an indicator of how close or far are the properties of the space from the structure of a linearly ordered space. Having in mind that the term interlocking nest is a key tool to a general solution of the orderability problem, we give a characterization of interlocking nest via closed sets in the Alexandroff topology and via lower sets, respectively. We also characterize bounded subsets of a given set in terms of nests and, finally, we explore the possibility of characterizing topological groups via properties of nests. All sections are followed by a number of open questions, which may give new directions to the orderability problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-18T17:52:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orderability problem",
      "open questions",
      "dual nests",
      "alexandroff topology",
      "lower sets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}