Algebraic structures in the sets of surjective functions

Abstract In the paper we construct several algebraic structures (vector spaces, algebras and free algebras) inside sets of different types of surjective functions. Among many results we prove that: the set of everywhere but not strongly everywhere surjective complex functions is strongly c -algebrable and that its 2 c -algebrability is consistent with ZFC; under CH the set of everywhere surjective complex functions which are Sierpinski–Zygmund in the sense of continuous but not Borel functions is strongly c -algebrable; the set of Jones complex functions is strongly 2 c -algebrable.