Analysis and Probability

Chapter 2

Topological Preliminaries

This chapter is motivated by the prominent role the topology plays in measure theory, and so in probability theory which may be viewed as a branch with specific problems and applications of measure theory. At the same time, comparing Chapter 2 with Chapter 3 shows the existence of certain similarities, that cannot be ignored, between some topological notions and some measure-theoretic notions, such as between topological space and measurable space, and between continuous function and measurable function. In this chapter we introduce and discuss most topological concepts we use in this book. Section 4 deals with methods of constructing topological spaces. In 5 and Section 6 we examine important properties of ...