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:
https://www.youtube.com/playlist?list=PLd8NbPjkXPliJunBhtDNMuFsnZPeHpm-0