## Lecture 6, September 24.

Material to be covered: Rudin Pages 36-39
Problem set 3 is due at 12 in 2.251.

Compactness

- Closed balls are closed
- Compact sets are closed, again
- Intersection of compact sets non-empty if finite intersections are.
- Infinite subsets of compact sets have limit points
- Intersection of decreasing sequence of non-empty closed intervals is non-empty