{
  "id": "1109.5307",
  "version": "v1",
  "published": "2011-09-24T20:58:11.000Z",
  "updated": "2011-09-24T20:58:11.000Z",
  "title": "Less than $2^ω$ many translates of a compact nullset may cover the real line",
  "authors": [
    "Márton Elekes",
    "Juris Steprāns"
  ],
  "journal": "Fund. Math. 181 (2004), no. 1, 89-96",
  "categories": [
    "math.LO",
    "math.CA"
  ],
  "abstract": "We answer a question of Darji and Keleti by proving that there exists a compact set $C_0\\subset\\RR$ of measure zero such that for every perfect set $P\\subset\\RR$ there exists $x\\in\\RR$ such that $(C_0+x)\\cap P$ is uncountable. Using this $C_0$ we answer a question of Gruenhage by showing that it is consistent with $ZFC$ (as it follows e.g. from $\\textrm{cof}(\\iN)<2^\\omega$) that less than $2^\\omega$ many translates of a compact set of measure zero can cover $\\RR$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-24T20:58:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28E15",
      "03E17",
      "03E35"
    ],
    "keywords": [
      "real line",
      "compact nullset",
      "translates",
      "compact set",
      "measure zero"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.5307E"
    }
  }
}