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

Márton Elekes, and Juris Steprāns. "Less than $2^{ω}$ many translates of a compact nullset may cover the real line." Fundamenta Mathematicae 181.1 (2004): 89-96. <http://eudml.org/doc/286453>.

@article{MártonElekes2004,
abstract = {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 $cof() < 2^\{ω\}$) that less than $2^\{ω\}$ many translates of a compact set of measure zero can cover ℝ.},
author = {Márton Elekes, Juris Steprāns},
journal = {Fundamenta Mathematicae},
keywords = {compact subset; measure zero; translate; cover; continuum; perfect set; consistence},
language = {eng},
number = {1},
pages = {89-96},
title = {Less than $2^\{ω\}$ many translates of a compact nullset may cover the real line},
url = {http://eudml.org/doc/286453},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Márton Elekes
AU - Juris Steprāns
TI - Less than $2^{ω}$ many translates of a compact nullset may cover the real line
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 1
SP - 89
EP - 96
AB - 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 $cof() < 2^{ω}$) that less than $2^{ω}$ many translates of a compact set of measure zero can cover ℝ.
LA - eng
KW - compact subset; measure zero; translate; cover; continuum; perfect set; consistence
UR - http://eudml.org/doc/286453
ER -