M ay 1 99 8 STRONGLY MEAGER SETS ARE NOT AN IDEAL
نویسندگان
چکیده
A set X ⊆ R is strongly meager if for every measure zero set H, X + H = R. Let SM denote the collection of strongly meager sets. We show that assuming CH, SM is not an ideal.
منابع مشابه
ar X iv : m at h / 99 05 12 0 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 BOREL IMAGES OF SETS OF REALS
The main goal of this paper is to generalize several results concerning cardinal invariants to the statements about the associated families of sets. We also discuss the relationship between the additive properties of sets and their Borel images. Finally, we present estimates for the size of the smallest set which is not strongly meager.
متن کاملar X iv : m at h / 99 07 13 7 v 1 [ m at h . L O ] 2 2 Ju l 1 99 9 STRONGLY MEAGER AND STRONG MEASURE ZERO SETS
In this paper we present two consistency results concerning the existence of large strong measure zero and strongly meager sets.
متن کامل2 7 N ov 2 00 1 STRONGLY MEAGER SETS CAN BE QUITE BIG
Lemma 1. 1. I is a σ-ideal, 2. I ⊆ (s)0, 3. I 6 = (s)0 (in ZFC). Notice that such a σ – ideal was defined and investigated in several papers, see for example [4]. Since strongly meager sets and strong measure zero sets are (s)0 it makes sense to ask if they are in I. It is well-known that SN ⊆ I. In fact, if F : 2 −→ 2 is a continuous function and X ∈ SN then F”(X) ∈ SN . The purpose of this pa...
متن کاملZero sets in pointfree topology and strongly $z$-ideals
In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...
متن کاملar X iv : m at h / 99 05 11 8 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 REMARKS ON SETS RELATED TO TRIGONOMETRIC SERIES
We show that several classes of sets, like N 0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.
متن کامل1 5 M ay 1 99 7 The null ideal restricted to some non null set may be א 1 - saturated
Our main result is that possibly some non-null set of reals cannot be divided to uncountably many non-null sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998