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

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dc.creatorElekes, Marton
dc.date2003-06-28
dc.date.accessioned2026-07-07T04:59:16Z
dc.date.available2026-07-07T04:59:16Z
dc.descriptionWe 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 $\RR$.
dc.description2 pages
dc.identifierhttps://arxiv.org/abs/math/0306411
dc.identifierhttp://arxiv.org/abs/math/0306411
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67914
dc.subjectGeneral Mathematics
dc.subjectLogic
dc.subject28E15, 03E17, 03E35
dc.titleLess than $2^/omega$ many translates of a compact nullset may cover the real line
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