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Less than $2^/omega$ many translates of a compact nullset may cover the real line

Marton Elekes
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Abstract

We answer a question of Darji and Keleti by proving in $ZFC$ that there exists a compact nullset $C_0\subset\RR$ 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 $ZFC$ that less than $2^ω$ many translates of a compact nullset cover $\RR$.

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Marton Elekes. 2003-06-28. Less than $2^/omega$ many translates of a compact nullset may cover the real line. https://arxiv.org/abs/math/0306411

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