On lineability of additive surjective functions

Abstract

We prove that the class of additive perfectly everywhere surjective functions contains (with the exception of the zero function) a vector space of maximal possible dimension ($2^\cont$). Additionally, we show under the assumption of regularity of $\cont$ that the family of additive everywhere surjective functions that are not strongly everywhere surjective contains (with the exception of the zero function) a vector space of dimension $\cont^+$.