Cardinal coefficients related to surjectivity, darboux, and sierpiński-zygmund maps

Abstract

We investigate the additivity A and lineability L cardinal coeffiients for the following classes of functions: ES\SES of everywhere surjective functions that are not strongly everywhere surjective, Darboux-like, Sierpinski-Zygmund, surjective, and their corresponding intersections. The classes SES and ES have been shown to be 2c-lineable. In contrast, although we prove here that ES\SES is c+-lineable, it is still unclear whether it can be proved in ZFC that ES\SES is 2c-lineable. Moreover, we prove that if c is a regular cardinal number, then A(ES\SES) ≤ c. This shows that, for the class ES\SES, there is an unusually large gap between the numbers A and L.