拓扑学(H)（2020春季学期）
中国科学技术大学数学科学学院
课程公告
(04/07) Welcome!
课程信息
授课老师：
王作勤 (wangzuoq at ustc dot edu dot cn)
上课时间：
星期一下午 14:00 – 15:35; 星期二下午 14:00-16:25； 星期四下午 15:55 – 18:20
上课地点：
ClassIn
办公室：
管研楼1601
助教：
Yiyu Wang(wangyiyu at mail dot ustc dot edu dot cn)
参考教材
James Munkres，拓扑学（第二版）
课程安排
课程安排可能会随着课程的进行而略有变动。
课程的讲义和习题将在每堂课后上传至bb系统。
作业在每周一午前交。
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| 序号 | 日期 | 内容 |
|---|---|---|
| Lecture 1 | 04/07 | Introduction: what is topology |
| Lecture 2 | 04/09 | Metrics spaces: examples and properties |
| Lecture 3 | 04/13 | Topology I: definitions and examples |
| Lecture 4 | 04/14 | Topology II: continuity, bases and subbases |
| Lecture 5 | 04/16 | Topology III: closed subsets and limit points |
| Lecture 6 | 04/20 | Compactness I |
| Lecture 7 | 04/21 | Compactness II |
| Lecture 8 | 04/24 | Compactness III |
| Lecture 9 | 04/26 | The axioms of countability |
| Lecture 10 | 04/27 | Separation axioms I |
| Lecture 11 | 04/28 | Separation axioms II |
| Lecture 12 | 04/30 | Paracompactness |
| Lecture 13 | 05/07 | Stone-Weierstrass Theoerem |
| Lecture 14 | 05/09 | Arzelá-Ascoli theorem |
| Lecture 15 | 05/11 | Connectedness |
| Lecture 16 | 05/12 | Path Connectedness and Homotopy |
| Lecture 17 | 05/14 | Fundamental groups I |
| Lecture 18 | 05/18 | Fundamental groups II |
| Lecture 19 | 05/19 | Fundamental groups III |
| Lecture 20 | 05/21 | Covering Spaces I |
| Lecture 21 | 05/25 | Covering Spaces II |
| Lecture 22 | 05/26 | Brouwer's Fixed point theorem |
| Lecture 23 | 05/28 | The Jordan curve theorem |
| Lecture 24 | 06/01 | Surfaces I |
| Lecture 25 | 06/02 | Surfaces II |
| Lecture 26 | 06/04 | Review |
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