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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67914We 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 $\RR$.2 pagesGeneral MathematicsLogic28E15, 03E17, 03E35Less than $2^/omega$ many translates of a compact nullset may cover the real linetext