Lecture 4, September 17.

1. Metric spaces, definition and examples - Euclidean metric, discrete metric and supremum metric.
2. Open balls in a metric space
3. Open subsets of a metric space
4. Unions and countable intersections of open sets are open
5. Open balls are open (duh)
6. Limit points and closed sets
7. Complements of closed sets are open and vice versa