{
  "id": "1901.06429",
  "version": "v1",
  "published": "2019-01-18T22:05:22.000Z",
  "updated": "2019-01-18T22:05:22.000Z",
  "title": "On Sets Containing an Affine Copy of Bounded Decreasing Sequences",
  "authors": [
    "Tongou Yang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "How small can a set be while containing many configurations? Following up on earlier work of Erd\\\"os and Kakutani \\cite{MR0089886}, Math\\'e \\cite{MR2822418} and M\\\"olter and Yavicoli \\cite{Molter}, we address the question in two directions. On one hand, if a subset of the real numbers contains an affine copy of all bounded decreasing sequences, then we show that such subset must be somewhere dense. On the other hand, given a collection of convergent sequences with prescribed decay, there is a closed and nowhere dense subset of the reals that contains an affine copy of every sequence in that collection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-18T22:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B05",
      "28A78",
      "28A12",
      "28A80"
    ],
    "keywords": [
      "bounded decreasing sequences",
      "affine copy",
      "sets containing",
      "real numbers contains",
      "earlier work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}