We define what it means to be a Hausdorff space. Then we show that in Hausdorff spaces finite sets are closed, limits of convergent sequences are unique, and neighborhoods of limit points intersect the limiting set in infinitely many points. 00:00 Introduction 00:19 Motivation for Hausdorff Property 08:58 Definition: Hausdorff Space 09:35 Example: Metric Spaces 13:00 Example: Discrete Spaces 14:18 Prop: Finite subsets of Hausdorff spaces are closed 19:42 Prop: Limits are unique in Hausdorff spaces 24:50 Prop: Neighborhoods of limit points contain infinitely many points of limiting set This lecture follows Lee's "Introduction to topological manifolds", chapter 2. A playlist with all the videos in this series can be found here:    • Topology