{
  "id": "2405.07112",
  "version": "v1",
  "published": "2024-05-12T00:03:56.000Z",
  "updated": "2024-05-12T00:03:56.000Z",
  "title": "Definable compactness in o-minimal structures",
  "authors": [
    "Pablo andújar Guerrero"
  ],
  "comment": "This is a round-up of the topological content of arXiv:2111.03802",
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types and definable downward directed families of closed sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-12T00:03:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "54A05",
      "54D30"
    ],
    "keywords": [
      "definable compactness",
      "o-minimal structures",
      "topological spaces",
      "answering questions",
      "definitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}