Arithmetic Operations on Functions from Sets into Functional Sets

In this paper x, X, X1, X2 are sets. Let Y be a functional set. The functor DOMS(Y ) is defined by: (Def. 1) DOMS(Y ) = ⋃ {dom f : f ranges over elements of Y }. Let us consider X. We say that X is complex-functions-membered if and only if: (Def. 2) If x ∈ X, then x is a complex-valued function. Let us consider X. We say that X is extended-real-functions-membered if and only if: (Def. 3) If x ∈ X, then x is an extended real-valued function. Let us consider X. We say that X is real-functions-membered if and only if: