拓扑学(H)（2024秋季学期）
中国科学技术大学数学科学学院
课程公告
(12/27) PSet 16, part 1 uploaded. Not to be turned in.
(12/27) PSet 16, part 2 uploaded. Not to be turned in.
(12/27) Final Exam Jan 08, 2025, 14:30-16:30 @ 5104 || Cover Lecture 1-Lecutre 30
课程信息
授课老师：
王作勤 (wangzuoq at ustc dot edu dot cn)
上课时间：
星期三上午 7:50am – 9:25am; 星期五下午 14:00am – 15:35am
上课地点：
五教 5206
办公室：
管研楼1601，少院303
助教：
Zhechen ZHANG (zhangzhechen at mail dot ustc dot edu dot cn)
Hao WANG (wang2262558615 at mail dot ustc dot edu dot cn)
答疑时间：
周日晚上
答疑地点：
5206
参考教材：
James Munkres，拓扑学（第二版）
教材：
王作勤，拓扑学讲义 （9月晚些时候发布）
课程安排，讲义以及习题
课程安排可能会随着课程的进行而略有变动。
作业每周发布，截止日期见作业本身（一般在周三），课前交。
| 序号 | 日期 | 内容 | 作业 |
|---|---|---|---|
| Lecture 1 | 09/04 | Introduction | PSet 1, part 1 : Due September 13. |
| Lecture 2 | 09/08 | Metric spaces | PSet 1, part 2 : Due September 13. |
| Lecture 3 | 09/11 | From metric to topology | PSet 2, part 1 : Due September 18. |
| Lecture 4 | 09/13 | Convergence and continuity | PSet 2, part 2 : Due September 18. |
| Lecture 5 | 09/18 | Construction of new topological spaces: basis and sub-basis | PSet 3, part 1 : Due September 25. |
| Lecture 6 | 09/20 | Construction of new topological spaces: induced and co-induced topology | PSet 3, part 2 : Due September 25. |
| Lecture 7 | 09/25 | Points and sets in topological space: Closed sets, limit points | PSet 4, part 1 : Due October 9. |
| Lecture 8 | 09/27 | Points and sets in topological space: Closure, interior, boundary | PSet 4, part 2 : Due October 9. | Lecture 9 | 10/09 | Compactness | PSet 5, part 1 : Due October 18. | Lecture 10 | 10/11 | Compactness of products | PSet 5, part 2 : Due October 18. | Lecture 11 | 10/12 | Compactness in metric space | PSet 6, part 1 : Due October 23. | Lecture 12 | 10/16 | Topologies on the space of mappings | PSet 6, part 2 : Due October 23. | Lecture 13 | 10/18 | Arzela-Ascoli theorem | PSet 7, part 1 : Due October 30. | Lecture 14 | 10/23 | Stone-Weierstrass theorem | PSet 7, part 2 : Due October 30. | 10/25 | No class （运动会） | Lecture 15 | 10/30 | Countability and separability | PSet 8, part 1 : Due November 08. | Lecture 16 | 11/1 | Urysohn lemma | PSet 8, part 2 : Due November 08. | Lecture 17 | 11/6 | Tietze extension | PSet 9, part 1 : Due November 15. | Lecture 18 | 11/8 | Paracompactness and partition of unity | PSet 9, part 2 : Due November 15. | 11/9 | Midterm@2103: Cover Lecture 1-Lecture 17 | Lecture 19 | 11/13 | Connectedness | PSet 10, part 1 : Due November 22. | Lecture 20 | 11/15 | Path Connectedness | PSet 10, part 2 : Due November 22. | Lecture 21 | 11/20 | Homotopy | PSet 11, part 1 : Due November 29. | Lecture 22 | 11/22 | Path homotopy and the fundamental group | PSet 11, part 2 : Due November 29. | Lecture 23 | 11/27 | The fundamental group of $S^n (n\ge 1)$ | PSet 12, part 1 : Due December 06. | Lecture 24 | 11/29 | Applications | PSet 12, part 2 : Due December 06. | Lecture 25 | 12/4 | Van Kampen Theorem | PSet 13, part 1 : Due December 13. | Lecture 26 | 12/6 | Covering space | PSet 13, part 2 : Due December 13. | Lecture 27 | 12/11 | Covering spaces v.s. the fundamental group | PSet 14, part 1 : Due December 20. | Lecture 28 | 12/13 | Brouwer fixed point theorem | PSet 14, part 2 : Due December 20. | Lecture 29 | 12/18 | Brouwer's invariance of domain theorem | PSet 15, part 1 : Due December 27. | Lecture 30 | 12/20 | Jordan curve theorem | PSet 15, part 2 : Due December 27. | Lecture 31 | 12/25 | Classification of curves | PSet 16, part 1 : Not to be turned in. | Lecture 32 | 12/27 | (Combinatorial) topology of compact surfaces | PSet 16, part 2 : Not to be turned in. | Lecture 33 | 1/3 | Classification of compact surfaces | 1/8 | Final Exam 14:30-16:30 @ 5104 || Cover Lecture 1-Lecutre 30 |
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