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

Marton Elekes

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

General Mathematics 2007-05-23 v1 Logic

Authors: Marton Elekes

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 $2^\omega$ many translates of a compact nullset cover $\RR$ .

Keywords

compact nullset translates real line perfect set ZFC covering

Cite

@article{arxiv.math/0306411,
  title  = {Less than $2^/omega$ many translates of a compact nullset may cover the real line},
  author = {Marton Elekes},
  journal= {arXiv preprint arXiv:math/0306411},
  year   = {2007}
}

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2 pages

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

Abstract

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