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 2c-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 c-algebrable; the set of Jones complex functions is strongly 2c-algebrable.
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