## Lecture 4, September 17.

Material to be covered: Rudin Pages 25-32

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