## 2017-09-02

### Undergraduate Topology by James Cook at Liberty University

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source: James Cook    2016年1月21日
Undergraduate Topology: These are from a short course based on Manetti's text. We hope to cover the essential topics in point set topology.

Undergraduate Topology: Jan 20, definition of topology, examples 59:51 Here we begin a short course in Topology. We're following Marco Manetti's text with insights added from Munkres and other things sitting around my office. There are three students in this course and they are of course responsible for my mistakes and oversights.
Keep in mind, this course is aimed at these three students in particular. They have already worked with metric topology in other coursework and the big picture of topology was covered in their previous class. I also decided to cover background material as we come to it.
Jan 20, definition of topology, examples part 2 18:58
Jan 27, Zariski topoology described, continuity 59:51
Jan 27, continuity, subspace topology (part 2) 21:40
Jan 29, nbhds, boundary points, continuity at pt (part 1) 59:51
Jan 29, nbhds, boundary points, continuity at pt (part 2) 25:55
Feb 3, immersion, product, Hausdorff (part 1) 59:51
Feb 3, immersion, product, Hausdorff (part 2) 34:24
Feb 7, connectedness (part 1) 59:51
Feb 7, connectedness (part 2) 35:54
Feb 10, connected components 25:18
Feb 17, theory of compact topologies (part 1) 59:51
Feb 17, theory of compact topologies (part 2) 21:46
Feb 19, topological groups (part 1) 59:51
Feb 19, topological groups (part 2) 29:16
Feb 24, identification maps 40:53
Feb 26, quotient topology (part 1) 59:51
Feb 26, quotient topology (part 2) 25:14
March 2, quotienting by group of homeomorphisms (part 1) 59:51
March 2, quotienting by group of homeomorphisms (part 2) 37:18
March 4, projective space (part 1) 35:53
March 4, projective space (part 2) 47:13
March 9, separable, 1 and 2 countable, sequences (part 1) 59:51
March 9, separable, 1 and 2 countable, sequences (part 2) 21:15
MVI 5959 59:51
March 11, totally bounded, T1-T4, etc. 34:55
April 1, existence theorem for ODEs 59:51
April 1, existence theorem for ODEs (part 2) 35:36
April 6, basic manifold theory (part 1) 59:51
April 6, basic manifold theory (part 2) 35:35
April 8, vector bundles and a word on fiber bundles (part 1) 59:51
April 8, global triviality, Riemannian Geometry begins (part 2) 29:40
April 27, supermath: introduction to supernumbers (part 1) 59:51
April 27, supermath: introduction to supernumbers (part 2) 16:29
May 4, a few words on supermanifolds 47:14