Continuous images of big sets and additivity of s0 under CPAprism

Authors

Krzysztof Ciesielski, West Virginia UniversityFollow

Document Type

Article

Publication Date

2004

College/Unit

Eberly College of Arts and Sciences

Department/Program/Center

Mathematics

Abstract

We prove that the Covering Property Axiom CPA_prism, which holds in the iterated perfect set model, implies the following facts.

• There exists a family G of uniformly continuous functions from R to [0,1] such that G has cardinality \omega₁ < \continuum and for every subset S of R of cardinality \continuum there exists a g in G with g[S]=[0,1].
• The additivity of the Marczewski's ideal s₀ is equal to \omega₁ < \continuum.

Digital Commons Citation

Ciesielski, Krzysztof, "Continuous images of big sets and additivity of s0 under CPAprism" (2004). Faculty & Staff Scholarship. 843.
https://researchrepository.wvu.edu/faculty_publications/843