We continue our discussion on quotient spaces, focusing on determining whether a given map is a quotient map.
00:00 Introduction
00:43 Recap: Quotient Spaces
04:22 Prop: Characterization of hausdorff quotients for open quotient maps
21:44 Def: Fibers / saturated subsets
24:05 Prop: Characterization of quotient maps using saturated sets
33:47 Properties of quotient maps
37:18 Example: Retracting R^n+1 to an n-sphere
42:00 Example: Embedding X into the cone over X
47:58 Example: Wrapping the unit interval around the circle
55:59 Prop: Open / Closed surjective maps are quotient maps
57:56 Prop: Summary of when open / closed maps are embeddings / quotient maps / homeomorphisms
This lecture follows Lee's "Introduction to topological manifolds", chapter 3.
A playlist with all the videos in this series can be found here:
https://www.youtube.com/playlist?list=PLd8NbPjkXPliJunBhtDNMuFsnZPeHpm-0