We define topological spaces and give examples including the discrete, trivial, and metric topologies. 00:00 Introduction 00:39 Reference and Prerequisites 02:17 Motivation: Familiar Spaces 10:22 Definition: Topological Space 19:59 Example: Discrete Topology 23:56 Example: Trivial Topology 27:51 Example: A Small Topology 32:41 Example: Metric Topology 37:21 Common Euclidean Subspaces 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