We construct Bernstein sets in ℝ having some additional algebraic properties. In particular, solving a problem of Kraszewski, Rałowski, Szczepaniak and Żeberski, we construct a Bernstein set which is a < c-covering and improve some other results of Rałowski, Szczepaniak and Żeberski on nonmeasurable sets.
@article{bwmeta1.element.doi-10_2478_s11533-009-0053-0,
author = {Marcin Kysiak},
title = {Bernstein sets with algebraic properties},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {725-731},
zbl = {1183.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0053-0}
}
Marcin Kysiak. Bernstein sets with algebraic properties. Open Mathematics, Tome 7 (2009) pp. 725-731. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0053-0/
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