2 7 N ov 2 00 1 STRONGLY MEAGER SETS CAN BE QUITE BIG
نویسنده
چکیده
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 paper is to show:
منابع مشابه
Strongly Meager Sets and Their Uniformly Continuous Images
We prove the following theorems: (1) Suppose that f : 2ω → 2ω is a continuous function and X is a Sierpiński set. Then (A) for any strongly measure zero set Y , the image f [X + Y ] is an s0-set, (B) f [X] is a perfectly meager set in the transitive sense. (2) Every strongly meager set is completely Ramsey null. This paper is a continuation of earlier works by the authors and by M. Scheepers (s...
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 کاملAn efficient implementation of Delaunay triangulations in medium dimensions
We propose a new C++ implementation of the well-known incremental algorithm for the construction of Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons have shown that our implementation outperforms the best currently available codes for convex hulls and Delaunay triangulations, and that it can be used for ...
متن کاملN ov 2 00 5 Equiangular lines , mutually unbiased bases , and spin models
We use difference sets to construct interesting sets of lines in complex space. Using (v, k, 1)-difference sets, we obtain k2−k+1 equiangular lines in Ck when k − 1 is a prime power. Using semiregular relative difference sets with parameters (k, n, k, λ) we construct sets of n + 1 mutually unbiased bases in Ck. We show how to construct these difference sets from commutative semifields and that ...
متن کاملN ov 2 00 7 Confidence intervals for the normal mean utilizing prior information
Consider X 1 , X 2 ,. .. , X n that are independent and identically N(µ, σ 2) distributed. Suppose that we have uncertain prior information that µ = 0. We answer the question: to what extent can a frequentist 1−α confidence interval for µ utilize this prior information?
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 2001