{
  "id": "2312.13047",
  "version": "v1",
  "published": "2023-12-20T14:18:50.000Z",
  "updated": "2023-12-20T14:18:50.000Z",
  "title": "On compact subsets of the reals",
  "authors": [
    "Wojciech Bielas",
    "Mateusz Kula",
    "Szymon Plewik"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological characterisation of compact sets of the reals. This allows us to reduce investigations of Cantorvals to properties of countable linear orders and to show, applying the Mazurkiewicz--Sierpi\\'nski Theorem (1920), that there exist continuum many non-homeomorphic L-Cantorvals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-20T14:18:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F65",
      "26A03",
      "54F05"
    ],
    "keywords": [
      "compact subset",
      "compact sets",
      "reduce investigations",
      "countable linear orders",
      "mazurkiewicz-sierpinski theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}