Topology Lecture 22: Compactness II

We prove important properties about compact subsets. 00:00 Introduction 01:40 Compact subsets of hausdorff spaces can be separated by open sets. 18:51 Tube lemma 33:09 Closes subsets of compact spaces are compact 38:48 Compact subsets of hausdorff spaces are closed 43:27 Compact subsets of metric spaces are bounded 49:13 Finite products of compact spaces are compact 57:26 Quotients of compact spaces are compact 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