Compositions of Two Additive Almost Continuous Functions

Authors

Krzysztof Ciesielski, West Virginia UniversityFollow

Document Type

Article

Publication Date

1997

College/Unit

Eberly College of Arts and Sciences

Department/Program/Center

Mathematics

Abstract

In the paper we prove that an additive Darboux function f : R → R can be expressed as a composition of two additive almost continuous (connectivity) functions if and only if either f is almost continuous (connectivity) function or dim(ker(f)) 6= 1. We also show that for every cardinal number λ ≤ 2 ω there exists an additive almost continuous functions with dim(ker(f)) = λ. A question whether every Darboux function f : R → R can be expressed as a composition of two almost continuous functions (see [?] or [?]) remains open.

Digital Commons Citation

Ciesielski, Krzysztof, "Compositions of Two Additive Almost Continuous Functions" (1997). Faculty & Staff Scholarship. 831.
https://researchrepository.wvu.edu/faculty_publications/831