Topological Preliminaries

As mentioned in the introduction, we shall present the theory of Borel sets in the general context of Polish spaces. In this chapter we give an account of Polish spaces. The space NN of sequences of natural numbers, equipped with the product of discrete topologies on N, is of particular importance to us. Our theory takes a particularly simple form on this space, and it is possible to generalize the results on Borel subsets of NN to general Polish spaces. The relevant results that we shall use to obtain these generalizations are presented in the last section of this chapter.