{
  "id": "1607.00517",
  "version": "v1",
  "published": "2016-07-02T14:48:16.000Z",
  "updated": "2016-07-02T14:48:16.000Z",
  "title": "On $σ$-countably tight spaces",
  "authors": [
    "István Juhász",
    "Jan van Mill"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $\\sigma$-countably tight compactum has cardinality $\\mathfrak{c}$ remains open. We also show that if an arbitrary product is $\\sigma$-countably tight then all but finitely many of its factors must be countably tight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-02T14:48:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "54B10"
    ],
    "keywords": [
      "countably tight spaces",
      "arbitrary countably tight subspaces",
      "cardinality",
      "infinite homogeneous compactum",
      "countably tight compactum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}