Small Combinatorial Cardinal Characteristics and Theorems of Egorov and Blumberg

Authors

Krzysztof Ciesielski, West Virginia UniversityFollow

Document Type

Article

Publication Date

2000

College/Unit

Eberly College of Arts and Sciences

Department/Program/Center

Mathematics

Abstract

We will show that the following set theoretical assumption

• \continuum=\omega₂, the dominating number d equals to \omega₁, and there exists an \omega₁-generated Ramsey ultrafilter on \omega

(which is consistent with ZFC) implies that for an arbitrary sequence f_n:R-->R of uniformly bounded functions there is a subset P of R of cardinality continuum and an infinite subset W of \omega such that {f_n|_P: n in W} is a monotone uniformly convergent sequence of uniformly continuous functions. Moreover, if functions f_n are measurable or have the Baire property then P can be chosen as a perfect set.

We will also show that cof(null)=\omega₁ implies existence of a magic set and of a function f:R-->R such that f|_D is discontinuous for every D which is not simultaneously meager and of measure zero.

Digital Commons Citation

Ciesielski, Krzysztof, "Small Combinatorial Cardinal Characteristics and Theorems of Egorov and Blumberg" (2000). Faculty & Staff Scholarship. 835.
https://researchrepository.wvu.edu/faculty_publications/835