Document Type
Article
Publication Date
1997
College/Unit
Eberly College of Arts and Sciences
Department/Program/Center
Mathematics
Abstract
For arbitrary families A and B of subsets of R let C(A,B)= {f| f: R-->R and the image f[A] is in B for every A in A} and C-1 (A,B)= {f| f: R-->R and the inverse image f-1(B) is in A for every B in B}. A family F of real functions is characterizable by images (preimages) of sets if F=C(A,B) (F=C-1(A,B), respectively) for some families A and B. We study which of classes of Darboux like functions can be characterized in this way. Moreover, we prove that the class of all Sierpinski-Zygmund functions can be characterized by neither images nor preimages of sets.
Digital Commons Citation
Ciesielski, Krzysztof, "Darboux Like Functions that are Characterizable by Images, Preimages and Associated Sets" (1997). Faculty & Staff Scholarship. 826.
https://researchrepository.wvu.edu/faculty_publications/826