Topology Lecture 21: Compactness I

We define compactness in terms of open covers and see several basic examples. We then prove that compactness is preserved by continuous functions.

00:00 Introduction
00:47 Definition: Open cover
05:22 Definition: Compactness
09:24 Examples of compact spaces
15:11 Compact subspace lemma
29:17 Convergent sequence is compact as subspace
36:52 Theorem: Continuous images of compact spaces are compact

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