Topology Lecture 24: Closed Map Lemma

We prove the closed map lemma, which states that every continuous map from a compact space to a hausdorff space is closed. Then we give two examples that show how to use the closed map lemma in the context of quotient spaces. 00:00 Introduction 00:20 Closed map lemma 24:25 Recap of universal property of quotient spaces 39:03 Quotient of unit interval is homeomorphic to the circle 47:50 Quotient of unit square is homeomorphic to torus 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