On meager additive and null additive sets in the Cantor space 2ω and in R

• Autorzy: Weiss T.
• Języki publikacji: EN

Abstrakty

EN

Let T be the standard Cantor-Lebesgue function that maps the Cantor space 2ω onto the unit interval (0,1). We prove within ZFC that for every X ⊆ 2ω, X is meager additive in 2ω iff T(X) is meager additive in (0,1). As a consequence, we deduce that the cartesian product of meager additive sets in R remains meager additive in R x R. In this note, we also study the relationship between null additive sets in 2ω and R.

Słowa kluczowe

EN

meager additive sets; null additive sets; translations in 2[omega] and in R

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 2
• Strony: 91--99
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Weiss T.

• Instytut Matematyki, Akademia Podlaska, 08-110 Siedlce,

Bibliografia

• [BJ] T. Bartoszyński and H. Judah, Set Theory, A K Peters, Wellesley, MA, 1995.
• [TW] B. Tsaban and T. Weiss, Products of special sets of real numbers, Real Anal. Exchange 30 (2004/2005), 1-17.