Spaces of Functions

Abstract

In this chapter, we will be investigating several types of spaces constructed from functions on a given space X to some other space Y. The spaces X and Y will usually be uniform spaces, but the theory of function spaces is more general than that. Much of this chapter, is independent of uniform spaces. The spaces we will study first will be needed in the next chapter to develop the concept of uniform differentiation. In fact, much of the content of this chapter and the next is needed simply to develop the machinery from classical analysis so that we can discuss uniform differentiation in isogeneous uniform spaces.