Lecture 6, September 24.

Problem set 3 is due at 12 in 2.251.

Compactness

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