{
  "id": "2207.01003",
  "version": "v1",
  "published": "2022-07-03T10:35:21.000Z",
  "updated": "2022-07-03T10:35:21.000Z",
  "title": "Algebraic structures on the Cantor set",
  "authors": [
    "Evgenii Reznichenko"
  ],
  "comment": "in Russian",
  "categories": [
    "math.GN"
  ],
  "abstract": "Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a Boolean precompact group; every strongly homogeneous space is rectifiable. In this case, the space can be embedded in the Cantor set with the preservation of the algebraic structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-03T10:35:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cantor set",
      "algebraic structure",
      "boolean precompact group",
      "open retract",
      "main results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}