Binary Operations

In this paper we define binary and unary operations on domains. number of schemes useful in justifying the existence of the operations are proved. The articles [3], [1], and [2] provide the notation and terminology for this paper. The arguments of the notions defined below are the following: f which is an object of the type Function; a, b which are objects of the type Any. The functor f .(a, b), with values of the type Any, is defined by it = f .a, b. One can prove the following proposition (1) for f being Function for a,b being Any holds f .(a, b) = f .a, b. In the sequel A, B, C will denote objects of the type DOMAIN. The arguments of the notions defined below are the following: A, B, C which are objects of the type reserved above; f which is an object of the type Function of [:A, B:], C; a which is an object of the type Element of A; b which is an object of the type Element of B. Let us note that it makes sense to consider the following functor on a restricted area. Then f .(a, b) is Element of C.