Abstract
The mapping or function concept, first introduced by the German mathematician and philosopher Leibniz, one of the founders of the calculus, is the central concept in modern mathematics. Without exaggeration the concept of function or mapping of one set into another is probably the single most important and universal notion that runs through all of mathematics [5]. This paper introduces two operations defined for a set of real-valued functions. One of the operations is motivated by a cover of the domain. The other operation is defined using the composition with Euclidean functions. Closure conditions with respect to the operations are defined and some of their properties are proved.