We define topological manifolds and topological manifolds with boundary. Then we introduce coordinate charts and atlases. Finally, we discuss how one would use topological invariants to prove invariance of dimension and invariance of boundary.
00:00 Introduction
00:16 Some spaces that may be manifolds
11:05 Definition: Locally Euclidean Spaces
16:24 Definition: Topological Manifold
19:42 Charts and Atlases for Manifolds
24:36 Thm: Invariance of Dimension
32:19 Motivation: Manifolds with Boundary
33:01 Definition: Upper Half-space
34:17 Definition: Topological Manifold with Boundary
40:38 Thm: Invariance of Boundary
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