Bernstein sets with algebraic properties
Open Mathematics (2009)
- Volume: 7, Issue: 4, page 725-731
- ISSN: 2391-5455
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topMarcin Kysiak. "Bernstein sets with algebraic properties." Open Mathematics 7.4 (2009): 725-731. <http://eudml.org/doc/269393>.
@article{MarcinKysiak2009,
abstract = {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.},
author = {Marcin Kysiak},
journal = {Open Mathematics},
keywords = {Bernstein set; κ-covering; Nonmeasurable set; -covering; nonmeasurable set},
language = {eng},
number = {4},
pages = {725-731},
title = {Bernstein sets with algebraic properties},
url = {http://eudml.org/doc/269393},
volume = {7},
year = {2009},
}
TY - JOUR
AU - Marcin Kysiak
TI - Bernstein sets with algebraic properties
JO - Open Mathematics
PY - 2009
VL - 7
IS - 4
SP - 725
EP - 731
AB - 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.
LA - eng
KW - Bernstein set; κ-covering; Nonmeasurable set; -covering; nonmeasurable set
UR - http://eudml.org/doc/269393
ER -
References
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- [2] Cichoń J., Jasiński A., Kamburelis A., Szczepaniak P., On translations of subsets of the real line, Fund. Math., 2002, 130(6), 1833–1842 Zbl0996.03031
- [3] Cichoń J., Szczepaniak P., When is the unit ball nonmeasurable?, preprint available at http://www.im.pwr.wroc.pl/~cichon/prace/UnitBall.zip. Zbl1221.28001
- [4] Kraszewski J., Rałowski R., Szczepaniak P., Żeberski Sz., Bernstein sets and κ-coverings, MLQ Math. Log. Q., in press, DOI: 10.1002/malq.200910008 [Crossref][WoS]
- [5] Kysiak M., Nonmeasurable algebraic sums of sets of reals, Colloq. Math., 2005, 102(1), 113–122 http://dx.doi.org/10.4064/cm102-1-10[Crossref] Zbl1072.28002
- [6] Muthuvel K., Application of covering sets, Colloq. Math., 1999, 80, 115–122 Zbl0931.26002
- [7] Nowik A., Some topological characterizations of omega-covering sets, Czechoslovak Math. J., 2000, 50(125), 865–877 http://dx.doi.org/10.1023/A:1022476915100[Crossref] Zbl1079.03547
- [8] Rałowski R., Szczepaniak P., Żeberski Sz., A generalization of Steinhaus theorem and some nonmeasurable sets, preprint available at http://www.im.pwr.wroc.pl/~zeberski/papers/raszze.pdf Zbl1225.03060
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