Complex Spaces 1

The articles [20], [16], [12], [1], [21], [5], [22], [7], [8], [3], [17], [11], [2], [18], [19], [6], [4], [9], [10], [15], [14], and [13] provide the notation and terminology for this paper. We follow the rules: k, n will be natural numbers, r, r , r1 will be real numbers, and c, c, c1, c2 will be elements of . In this article we present several logical schemes. The scheme FuncDefUniq concerns a non-empty set A, a non-empty set B, and a unary functor F yielding an element of B and states that: for all functions f1, f2 from A into B such that for every element x of A holds f1(x) = F(x) and for every element x of A holds f2(x) = F(x) holds f1 = f2 for all values of the parameters. The scheme UnOpDefuniq deals with a non-empty set A and a unary functor F yielding an element of A and states that: for all unary operations u1, u2 on A such that for every element x of A holds u1(x) = F(x) and for every element x of A holds u2(x) = F(x) holds u1 = u2 for all values of the parameters. The scheme BinOpDefuniq deals with a non-empty setA and a binary functor F yielding an element of A and states that: for all binary operations o1, o2 on A such that for all elements a, b of A holds o1(a, b) = F(a, b) and for all elements a, b of A holds o2(a, b) = F(a, b) holds o1 = o2 for all values of the parameters.