ADDITIVE SIERPIŃSKI-ZYGMUND FUNCTIONS.

In the paper we present an exhaustive discussion of the relations between Darboux-like functions within the class of additive Sierpiński-Zygmund (SZ) functions. In particular, we give an example of an additive Sierpiński-Zygmund (SZ) injection f : ℝ → ℝ such that f-1 is not an SZ function. Under the assumption that R cannot be covered by less than c-many meager sets we give examples of an additive SZ bijection f : ℝ → ℝR such that f-1 is not SZ and of an additive injection f : ℝ → ℝ such that both f and f-1 are SZ. [ABSTRACT FROM AUTHOR]