**Definitions:**

3.22 (equivalent norms)

3.26 (relatively open set)

4.1 (convergent sequence)

4.30 (limsup and liminf)

5.1 (Cauchy sequence)

5.4 (complete metric space)

**Suggested Review Problems/Exercises:**

Section 3:

Problem 3.5

Section 4:

Exercises 4.5, 4.7, 4.8, 4.11, 4.13

Problems 4.5, 4.6, 4.7, 4.8, 4.10, 4.12, 4.15

Section 5:

Exercises: 5.2, 5.4

Problems: 5.1