Chapter 8: Metric spaces

1. Definition and examples; normed vector spaces
2. Convergence and continuity
3. Open and closed sets
4. Completeness
5. Compactness (sequential); properties of compact sets
6. Continuous functions on compact sets
7. Heine Borel Theorem
Definition of the Riemann-Stieltjes integral
8. Connected sets; path connected sets; continuous images