Less than $2^{ω}$ many translates of a compact nullset may cover the real line

• Autorzy: Márton Elekes , Juris Steprāns
• Języki publikacji: EN

Abstrakty

EN

We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from $cof(𝓝) < 2^{ω}$) that less than $2^{ω}$ many translates of a compact set of measure zero can cover ℝ.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 28E15: Other connections with logic and set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 1
• Strony: 89-96

Daty

wydano

2004

Twórcy

autor

Márton Elekes

• Rényi Alfréd Institute, Reáltanoda u. 13-15, Budapest, 1053, Hungary

autor

Juris Steprāns

• Department of Mathematics, York University, Toronto, Ontario, M3J 1P3, Canada

Identyfikatory

DOI

10.4064/fm181-1-4