Topology Lecture 05: Homeomorphism скачать в хорошем качестве

Topology Lecture 05: Homeomorphism

We define homeomorphisms between topological spaces and show that this induces a bijection of the open sets of the spaces. We then give three examples of homeomorphisms, which show that neither size nor boundedness are topological properties. 00:00 Introduction 00:23 Definition: Homeomorphism 06:05 Prop: Characterization of Homeomorphism 19:52 Example: Open balls are homeomorphic 26:44 Example: Unit ball is homeomorphic to R^n 36:55 Example: Cube is homeomorphic to sphere 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