Geodesic
Covering the real line with translates of a zero-dimensional compact set
András Máthé1
1 Alfréd Rényi Institute of Mathematics Reáltanoda u. 13-15 1053 Budapest, Hungary and Department of Mathematics University of Warwick Coventry, CV4 7AL, UK
Fundamenta Mathematicae, Tome 213 (2011) no. 3, pp. 213-219 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm213-3-2
Keywords: construct compact set hausdorff dimension zero cof mathcal many translates cover real line hence consistent zfc continuum many translates zero dimensional compact set cover real line answers question dan nbsp mauldin

András Máthé 1

1 Alfréd Rényi Institute of Mathematics Reáltanoda u. 13-15 1053 Budapest, Hungary and Department of Mathematics University of Warwick Coventry, CV4 7AL, UK 
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András Máthé. Covering the real line with translates of a zero-dimensional compact set. Fundamenta Mathematicae, Tome 213 (2011) no. 3, pp. 213-219. doi: 10.4064/fm213-3-2

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