Topology Lecture 03: Convergence

We define limit points, isolated points, dense subsets, and convergent sequences in a general topological space. 00:00 Introduction 00:34 Definition: Limit Point of a Set 05:00 Example: Limit Points of (0,1) 11:48 Definition: Isolated Point 12:55 Example: Every point of sequence 1/n is isolated 18:29 Definition: Dense Subset 21:43 Prop: Characterization of Dense Subsets 25:01 Definition: Convergent Sequence 28:32 Prop: Limits lie in closure This lecture follows Lee's "Introduction to topological manifolds", chapter 2. A playlist with all the videos in this series can be found here: https://www.youtube.com/playlist?list=PLd8NbPjkXPliJunBhtDNMuFsnZPeHpm-0