{
  "id": "2004.10689",
  "version": "v1",
  "published": "2020-04-15T10:09:07.000Z",
  "updated": "2020-04-15T10:09:07.000Z",
  "title": "A (co)homology theory for some preordered topological spaces",
  "authors": [
    "Manuel Norman"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting from the preorder, and then to consider some (co)homology for the obtained poset; however, we will prove that every topological space with the above preorder consists of two disjoint parts (one called 'poset part', and the other one called 'complementary part', which is not a poset in general): this suggests an improvement of the previous method that also takes into account the poset part, and this is indeed what we will study here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-15T10:09:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A11",
      "55U10"
    ],
    "keywords": [
      "homology theory",
      "preordered topological spaces",
      "poset part",
      "partial order",
      "preorder consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}