{
  "id": "2204.02457",
  "version": "v1",
  "published": "2022-04-05T19:16:36.000Z",
  "updated": "2022-04-05T19:16:36.000Z",
  "title": "An answer to a question of J.W. Cannon and S.G. Wayment",
  "authors": [
    "Olga Frolkina"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "Solving R.J. Daverman's problem, V. Krushkal described sticky Cantor sets in $\\mathbb R^N$ for $N\\geqslant 4$; these sets cannot be isotoped off of itself by small ambient isotopies. Using Krushkal sets, we answer a question of J.W. Cannon and S.G. Wayment (1970). Namely, for $N\\geqslant 4$ we construct compacta $X\\subset \\mathbb R^N$ with the following two properties: some sequence $\\{ X_i \\subset \\mathbb R^N \\setminus X, \\ i\\in\\mathbb N \\}$ converges homeomorphically to $X$, but there is no uncountable family of pairwise disjoint sets $Y_\\alpha \\subset \\mathbb R^N$ each of which is embedded equivalently to $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-05T19:16:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N35",
      "57N45",
      "57M30"
    ],
    "keywords": [
      "sticky cantor sets",
      "small ambient isotopies",
      "krushkal sets",
      "pairwise disjoint sets",
      "davermans problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}