{
  "id": "1605.00853",
  "version": "v1",
  "published": "2016-05-02T17:05:22.000Z",
  "updated": "2016-05-02T17:05:22.000Z",
  "title": "A primitive associated to the Cantor-Bendixson derivative on the real line",
  "authors": [
    "Borys Álvarez-Samaniego",
    "Andrés Merino"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We consider the class of compact countable subsets of the real numbers $\\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof of a result shown by S. Mazurkiewicz and W. Sierpinski related to the cardinality of this partition. Furthermore, for any compact subset of $\\mathbb{R}$, we show the existence of a \"primitive\" related to its Cantor-Bendixson derivative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-02T17:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "03E15"
    ],
    "keywords": [
      "real line",
      "cantor-bendixson derivative",
      "compact countable subsets",
      "real numbers",
      "appropriate partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}