Covering the real line with translates of a zero-dimensional compact set

Volume 213 / 2011

András Máthé Fundamenta Mathematicae 213 (2011), 213-219 MSC: Primary 28A78; Secondary 03E17, 03E35. DOI: 10.4064/fm213-3-2


We construct a compact set $C$ of Hausdorff dimension zero such that ${\rm cof}(\mathcal N)$ many translates of $C$ cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.


  • András MáthéAlfréd Rényi Institute of Mathematics
    Reáltanoda u. 13-15
    1053 Budapest, Hungary
    Department of Mathematics
    University of Warwick
    Coventry, CV4 7AL, UK

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