Lecture 6, September 24.

Material to be covered: Rudin Pages 36-39

Problem set 3 is due at 12 in 2.251.


  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