We define compact sets for ℝ as closed and bounded sets, give some examples, and then give different characterizations in terms of limits of sequences and open covers.
0:00, Intro
0:38, Definition of Compactness
5:44, Theorem: Limit Compactness
8:48, Definition of Open Cover/Finite Subcover
15:33, Theorem: Compactness and Open Covers
