{
  "id": "2004.08760",
  "version": "v1",
  "published": "2020-04-19T03:41:03.000Z",
  "updated": "2020-04-19T03:41:03.000Z",
  "title": "Maximal almost disjoint families and pseudocompactness of hyperspaces",
  "authors": [
    "Osvaldo Guzmán",
    "Michael Hrušák",
    "Vinicius de Oliveira Rodrigues",
    "Stevo Todorčević",
    "Artur Hideyuki Tomita"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if $\\mathsf{MA}_\\mathfrak c (\\mathcal P(\\omega)/\\mathrm{fin})$ holds. We further study the question whether there is a maximal almost disjoint family whose hyperspace is pseudocompact and prove that consistently such families do not exist \\emph{genericaly}, by constructing a consistent example of a maximal almost disjoint family $\\mathcal A$ of size less than $\\mathfrak c$ whose hyperspace is not pseudocompact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-19T03:41:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "03E35",
      "54D35",
      "03E17"
    ],
    "keywords": [
      "disjoint family",
      "pseudocompactness",
      "pseudocompact vietoris hyperspace",
      "consistent example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}