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 $\cont^+$.
Citation
Krzysztof Płotka. "On lineability of additive surjective functions." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 633 - 639, november 2019. https://doi.org/10.36045/bbms/1576206361
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