{
  "id": "2306.11712",
  "version": "v1",
  "published": "2023-06-20T17:42:06.000Z",
  "updated": "2023-06-20T17:42:06.000Z",
  "title": "On two consequences of CH established by Sierpiński",
  "authors": [
    "Roman Pol",
    "Piotr Zakrzewski"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the relations between two consequences of the Continuum Hypothesis discovered by Wac{\\l}aw Sierpi\\'nski, concerning uniform continuity of continuous functions and uniform convergence of sequences of real-valued functions, defined on subsets of the real line of cardinality continuum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-20T17:42:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E20",
      "03E15",
      "26A15",
      "54C05"
    ],
    "keywords": [
      "consequences",
      "sierpiński",
      "real line",
      "uniform convergence",
      "continuum hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}