Algebraic structures in the sets of surjective functions

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 cc-algebrable and that its 2c2c-algebrability is consistent with ZFC; under CH   the set of everywhere surjective complex functions which are Sierpiński–Zygmund in the sense of continuous but not Borel functions is strongly cc-algebrable; the set of Jones complex functions is strongly 2c2c-algebrable.