Sequences in Metric Spaces

Sequences of real numbers and their limits play a large role in calculus and in applied mathematics. In this chapter you will study sequences in the broader context of metric spaces, but the results, of course, apply to sequences of real numbers. The chapter begins with a careful study of sequences in general and then passes to metric spaces where the concept of limit can be introduced. This is followed by a look at how sequences are related to metric properties, like closure or continuity. Finally, there is a brief study of Cauchy sequences and complete metric spaces.