Maximal additive families for some classes of Darboux functions (Q1106962)

We consider real functions defined on the real line. For a family F of such functions, let M(F) denote the family of all g such that \(f\in F\) implies \(f+g\in F\). The author determines M(F) for \(F=D^ c,D^*,D^{**},\) where \(D^ c\) is the family of Darboux functions having continuous upper and lower boundary functions, \(D^*(D^{**})\) is the family of the functions that take on every real value \((2^{\omega}\) times) in every interval.