Covering the real line with translates of a zero-dimensional compact set
András Máthé
Fundamenta Mathematicae, Tome 215 (2011), p. 213-219 / Harvested from The Polish Digital Mathematics Library
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We construct a compact set C of Hausdorff dimension zero such that cof(𝒩) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:286246 
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András Máthé. Covering the real line with translates of a zero-dimensional compact set. Fundamenta Mathematicae, Tome 215 (2011) pp. 213-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-2/