Covering the real line with translates of a zero-dimensional compact set

• Autorzy: András Máthé
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 28A78: Hausdorff and packing measures
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 3
• Strony: 213-219

Daty

wydano

2011

Twórcy

autor

András Máthé

• Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, 1053 Budapest, Hungary
• Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

Identyfikatory

DOI

10.4064/fm213-3-2