Continuous Images of Sets of Reals

نویسنده

  • TOMEK BARTOSZYNSKI
چکیده

We will show that, consistently, every uncountable set can be continuously mapped onto a non measure zero set, while there exists an uncountable set whose all continuous images into a Polish space are meager.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Combinatorial images of sets of reals and semifilter trichotomy

Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the of the Hurewicz 1927 problem is po...

متن کامل

Decomposition of supra soft locally closed sets and supra SLC-continuity

In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [{it International Journal of Mathematical Trends and Technology} (IJMTT), (2014) Vol. 9 (1):37--...

متن کامل

Point-cofinite Covers in the Laver Model

Let S1(Γ,Γ) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Γ,Γ). We prove the following assertions: (1) If there is an unbounded tower, then there are sets of reals of cardinality b, satisfying S1(Γ,Γ). (2) It is consistent that all set...

متن کامل

Diagonalization of continuous matrices as a representation of intuitionistic reals

We use topological models of intuitionistic analysis to answer some of the recent questions of Kadison [7] concerning diagonalization of matrices of continuous functions. Let X be a compact Hausdorff space, and let %(X) be the ring of continuous real functions on X. In the topological interpretation of intuitionistic analysis over X [3], %(X) represents the internal set of (Dedekind) reals. Thu...

متن کامل

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 کامل

ذخیره 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 2000