ABSTRACT
We begin by developing the concept of distance between elements of a space X. We remind the reader that, as noted in the introduction to this chapter, we will generally limit our attention to the sets R, Rk, and C. As we saw in the previous chapter, each of these spaces is a normed space. Since most of the results of interest to us will apply to all of them, we will let X be our concise notation for any (or all) of these spaces in statements that apply to them all. With this convention in mind, we note that the norm associated with a space is a convenient means for measuring distances between points in that space.1
This motivates the following definition:
