{
  "id": "2212.02372",
  "version": "v1",
  "published": "2022-12-05T15:53:50.000Z",
  "updated": "2022-12-05T15:53:50.000Z",
  "title": "A new simple family of Cantor sets in $\\mathbb{R}^3$ all of whose projections are one-dimensional",
  "authors": [
    "Olga Frolkina"
  ],
  "journal": "Topol. Appl. 288 (2021) 107452",
  "doi": "10.1016/j.topol.2020.107452",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "In 1994, J.Cobb described a Cantor set in $\\mathbb{R}^3$ each of whose projections into 2-planes is one-dimensional. A series of works by other authors developing this field followed. We present another very simple series of Cantor sets in $\\mathbb{R}^3$ all of whose projections are connected and one-dimensional. These are self-similar Cantor sets which go back to the work of Louis Antoine, and we celebrate their centenary birthday in 2020-2021.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T15:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F45",
      "57N12",
      "28A80"
    ],
    "keywords": [
      "projections",
      "one-dimensional",
      "simple family",
      "self-similar cantor sets",
      "simple series"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}