{
  "id": "2212.02983",
  "version": "v1",
  "published": "2022-12-05T17:50:32.000Z",
  "updated": "2022-12-05T17:50:32.000Z",
  "title": "Pairwise disjoint Moebius bands in space",
  "authors": [
    "Olga Frolkina"
  ],
  "journal": "J. of Knot Theory and its Ramif. 27 (2018) 9, art.1842005",
  "doi": "10.1142/S0218216518420051",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "V.V.Grushin and V.P.Palamodov proved in 1962 that it is impossible to place in $R^3$ uncountably many pairwise disjoint polyhedra each homeomorphic to the Moebius band. We generalize this result in two directions. First, we give a generalization of this result to tame subsets in $R^N$, $N\\geqslant 3$. Second, we show that in case of $R^3$ the theorem holds for arbitrarily topologically embedded (not necessarily tame) Moebius bands.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T17:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M30",
      "57N35",
      "54C25"
    ],
    "keywords": [
      "pairwise disjoint moebius bands",
      "theorem holds",
      "tame subsets",
      "pairwise disjoint polyhedra",
      "necessarily tame"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}