ABSTRACT
So far we have dealt only with finite dimensional vector spaces, In this chapter we extend the ideas of Chapter 1 to vector spaces without finite dimension. We begin by defining a linear vector space, as before, to be a collection of objects, S, which are closed under addition and scalar multiplication. That is, if x and y are in S, and α is a real (or complex) number, then x + y is in S and αx is in S. Next, we want our space to have a norm, or measure of size, in which case we have a normed linear vector space.
