Topology Lecture 23: Compactness III

We prove that closed, bounded intervals of the real line are compact, along with the Heine-Borel theorem, and the extreme value theorem. 00:00 Introduction 03:17 Closed & bounded intervals are compact 23:03 Heine-Borel: The compact subsets of R^n are exactly the closed & bounded ones 29:17 Extreme value theorem This lecture follows Lee's "Introduction to topological manifolds", chapter 4. A playlist with all the videos in this series can be found here:    • Topology