#### 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