Covering the real line with translates of a zero-dimensional compact set
Volume 213 / 2011
Fundamenta Mathematicae 213 (2011), 213-219
MSC: Primary 28A78; Secondary 03E17, 03E35.
DOI: 10.4064/fm213-3-2
Abstract
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.
