Bernstein sets with algebraic properties

• Autorzy: Marcin Kysiak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bernstein set; κ-covering; Nonmeasurable set

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 20K99: None of the above, but in this section
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 725-731

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Marcin Kysiak

• Institute of Mathematics, University of Warsaw, Warsaw, Poland

Bibliografia

• [1] Carlson T.J., Strong measure zero and strongly meager sets, Proc. Amer. Math. Soc., 1993, 118(2), 577–586 http://dx.doi.org/10.2307/2160341[Crossref]
• [2] Cichoń J., Jasiński A., Kamburelis A., Szczepaniak P., On translations of subsets of the real line, Fund. Math., 2002, 130(6), 1833–1842
• [3] Cichoń J., Szczepaniak P., When is the unit ball nonmeasurable?, preprint available at http://www.im.pwr.wroc.pl/~cichon/prace/UnitBall.zip.
• [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]
• [6] Muthuvel K., Application of covering sets, Colloq. Math., 1999, 80, 115–122
• [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]
• [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

Identyfikatory

DOI

10.2478/s11533-009-0053-0