### Covering locally compact groups by less than ${2}^{\omega}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if ${C}_{EK}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of ${C}_{EK}$. As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...