共查询到20条相似文献，搜索用时 15 毫秒
1.
In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ?2 and ?. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Marek Balcerzak Joanna Peredko 《Proceedings of the American Mathematical Society》1999,127(9):2759-2766
For we obtain new theorems stating that a Borel set in with large sets of large vertical and large horizontal sections admits a one-to-one Borel selection with large domain and large range. Largeness is meant mainly in measure or category sense. Our proofs combine a result of Graf and Mauldin with a modified result of Sarbadhikari.
3.
We consider several natural situations where the union or intersection of an uncountable family of measurable (in various senses) sets with a good additional structure is again measurable or may fail to be measurable. We primarily deal with Lebesgue measurable sets and sets with the Baire property. In particular, uncountable unions of sets homeomorphic to a closed Euclidean simplex are considered in detail, and it is shown that the Lebesgue measure and the Baire property differ essentially in this aspect. Another difference between measure and category is illustrated in the case of some uncountable intersections of sets of full measure (comeager sets, respectively). We also discuss a topological form of the Vitali covering theorem, in connection with the Baire property of uncountable unions of certain sets. 相似文献
4.
In this paper we define certain types of projections of planar sets and study some properties of such projections. 相似文献
5.
We discuss the question of which properties of smallness in the sense of measure and category (e.g. being a universally null, perfectly meager or strongly null set) imply the properties of smallness related to some tree forcing notions (e.g. the properties of being Laver-null or Miller-null).
6.
Tomek Bartoszynski Saharon Shelah 《Proceedings of the American Mathematical Society》2002,130(12):3701-3711
We will show that there is no example of a set distinguishing between universally null and perfectly meager sets.
7.
We prove the following theorems:
(1) Suppose that is a continuous function and is a Sierpinski set. Then
- (A)
- for any strongly measure zero set , the image is an -set,
- (B)
- is a perfectly meager set in the transitive sense.
(2) Every strongly meager set is completely Ramsey null.
8.
R. Filipów 《Acta Mathematica Hungarica》2003,100(1-2):97-104
We show that it is consistent with ZFC that the family of functions with the Baire property has the difference property. That
is, every function for which f(x + h)-f(x) has the Baire property for every h∈R is of the form f=g + Awhere g has the Baire property and A is additive.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
We study the role the axiom of choice plays in the existence of some special subsets of ? and its power set ?(?). 相似文献
10.
We prove the following two theorems.
then .
Theorem 1. Let be a strongly meager subset of . Then it is dual Ramsey null.
We will say that a -ideal of subsets of satisfies the condition iff for every , if
then .
Theorem 2. The -ideals of perfectly meager sets, universally meager sets and perfectly meager sets in the transitive sense satisfy the condition .
11.
Robert Rałowski 《Mathematical Logic Quarterly》2009,55(6):659-665
We show that under some conditions on a family A ? I there exists a subfamily A0 ? A such that ∪ A0 is nonmeasurable with respect to a fixed ideal I with Borel base of a fixed uncountable Polish space. Our result applies to the classical ideal of null subsets of the real line and to the ideal of first category subsets of the real line (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
13.
Stuart Zoble 《Proceedings of the American Mathematical Society》2008,136(5):1807-1814
There is a well-known global equivalence between sets having the universal Baire property, two-step generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of sets being -cc-universally Baire, which is below . In a model obtained, there is a set which is weakly -universally Baire but not -universally Baire.
14.
Lorenz Halbeisen 《Mathematical Logic Quarterly》2003,49(2):173-178
For a ? b ? ω with b a infinite, the set D = {x ∈ [ω]ω : a ? x ? b} is called a doughnut. A set S ? [ω]ω has the doughnut property ?? if it contains or is disjoint from a doughnut. It is known that not every set S ? [ω]ω has the doughnut property, but S has the doughnut property if it has the Baire property ?? or the Ramsey property ?. In this paper it is shown that a finite support iteration of length ω1 of Cohen forcing, starting from L , yields a model for CH + (??) + (??) + (?). 相似文献
15.
Janusz Pawlikowski 《Proceedings of the American Mathematical Society》1998,126(10):3083-3087
We give a forcing free proof of a conjecture of Mycielski that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the continuum.
16.
In this paper, we study the modified box dimensions of cut-out sets that belong to a positive, nonincreasing and summable sequence. Noting that the family of such sets is a compact metric space under the Hausdorff metric, we prove that the lower modified box dimension equals zero and the upper modified box dimension equals the upper box dimension for almost all cut-out set in the sense of Baire category. 相似文献
17.
Gary Gruenhage David Lutzer 《Proceedings of the American Mathematical Society》2000,128(10):3115-3124
In this paper we describe broad classes of spaces for which the Baire space property is equivalent to the assertion that any two dense -sets have dense intersection. We also provide examples of spaces where the equivalence does not hold. Finally, our techniques provide an easy proof of a new internal characterization of perfectly meager subspaces of and characterize metric spaces that are always of first category.
18.
S. Basu 《Czechoslovak Mathematical Journal》2000,50(1):59-65
Steinhaus [9] prove that if a set A has a positive Lebesgue measure in the line then its distance set contains an interval. He obtained even stronger forms of this result in [9], which are concerned with mutual distances between points in an infinite sequence of sets. Similar theorems in the case we replace distance by mutual ratio were established by Bose-Majumdar [1]. In the present paper, we endeavour to obtain some results related to sets with Baire property in locally compact topological spaces, particular cases of which yield the Baire category analogues of the above results of Steinhaus [9] and their corresponding form for ratios by Bose-Majumdar [1]. 相似文献
19.
Tomek Bartoszynski 《Proceedings of the American Mathematical Society》2003,131(2):625-630
We show that the Dual Borel Conjecture implies that boldsymbolaleph_1 $\"> and find some topological characterizations of perfectly meager and universally meager sets.
20.
Jacek Cichon Andrzej Jasinski Anastasis Kamburelis Przemyslaw Szczepaniak 《Proceedings of the American Mathematical Society》2002,130(6):1833-1842
In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpinski. We discuss the number of translations a single subset of the reals may have. Later we discuss almost invariant subsets of Abelian groups.