{
  "id": "2006.12675",
  "version": "v1",
  "published": "2020-06-23T00:20:41.000Z",
  "updated": "2020-06-23T00:20:41.000Z",
  "title": "Countably compact groups without non-trivial convergent sequences",
  "authors": [
    "Michael Hrušák",
    "Jan van Mill",
    "Ulises Ariet Ramos-García",
    "Saharon Shelah"
  ],
  "comment": "21 pages, to be published in Transactions of the American Mathematical Society",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We construct, in $\\mathsf{ZFC}$, a countably compact subgroup of $2^{\\mathfrak{c}}$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\\mathbb{G}_{0}$ and $\\mathbb{G}_{1}$ such that the product $\\mathbb{G}_{0} \\times \\mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-23T00:20:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "03C20",
      "03E05",
      "54H11"
    ],
    "keywords": [
      "non-trivial convergent sequences",
      "countably compact groups",
      "van douwen",
      "countably compact subgroup",
      "old problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}