拓扑学(H)（2022春季学期）


中国科学技术大学数学科学学院

[课程公告] [课程信息] [课程安排，讲义以及习题]

课程公告

o (06/18)Final ExamROOM CHANGE ：June 21, 8:30-10:30 @ Room 2103. Cover Lecture 1 - Lecture 29. .

课程信息

o 授课老师：   王作勤 (wangzuoq at ustc dot edu dot cn)

o 上课时间：   星期一上午 9:45am – 12:10pm; 星期三下午 14:00am – 15:35am　

o 上课地点：   二教 2406

o 办公室：   管研楼1601

o 助教：   Hanzhang YUN (yhzz123yhzz at mail dot ustc dot edu dot cn)

o 答疑时间：   星期六晚上，19:30-21:00

o 答疑地点：   管研楼1308

o 参考教材：   James Munkres，拓扑学（第二版）

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课程安排，讲义以及习题

o 课程安排可能会随着课程的进行而略有变动。

o 课程的讲义将在每堂课后上传。

o 作业在每周一课前交。

序号 日期 内容 讲义 作业
  Lecture 1     02/21     Introduction     Lect 1     PSet 1, part 1   : Due February 28.
  Lecture 2     02/23     Metrics spaces     Lect 2     PSet 1, part 2   : Due February 28.
  Lecture 3     02/28     Topology spaces: definitions and examples     Lect 3     PSet 2, part 1   : Due March 07.
  Lecture 4     03/02     Convergence and continuity in topological spaces     Lect 4     PSet 2, part 2   : Due March 07.
  Lecture 5     03/07     Bases and sub-bases, induced and co-induced topology     Lect 5     PSet 3, part 1   : Due March 14.
  Lecture 6     03/09     Quotient topology, group actions     Lect 6     PSet 3, part 2   : Due March 14.
  Lecture 7     03/14     Points and sets in topological space     Lect 7     PSet 4, part 1   : Due March 21.
  Lecture 8     03/16     Compactness     Lect 8     PSet 4, part 2   : Due March 21.
  Lecture 9     03/21     Compactness of product space, Tychonoff theorem     Lect 9     PSet 5, part 1   : Due March 28.
  Lecture 10     03/23     Compactness in metric space     Lect 10     PSet 5, part 2   : Due March 28.
  Lecture 11     03/28     Compactness in the space of continuous maps: Arzela-Ascolli theorem     Lect 11     PSet 6, part 1   : Due April 06.
  Lecture 12     03/30     The algebra of functions: Stone-Weierstrass theorem     Lect 12     PSet 6, part 2   : Due April 06.
  Lecture 13     04/02     Countability and Separation Axioms     Lect 13     PSet 7, part 1   : Due April 11.
  Lecture 14     04/06     Urysohn lemma and Urysohn metrization theorem     Lect 14     PSet 7, part 2   : Due April 11.
  Lecture 15     04/11     Tietze extension theorem and applications     Lect 15     PSet 8, part 1   : Due April 18.
  Lecture 16     04/13     Paracompactness and partition of unity     Lect 16     PSet 8, part 2   : Due April 18.
      04/18     Midterm: Cover Lecture 1-Lecutre 16 @ 1102      
  Lecture 17     04/20     Connectedness     Lect 17     PSet 9, part 1   : Due May 04.
  Lecture 18     04/25     Path connecteness     Lect 18     PSet 9, part 2   : Due May 04.
  Lecture 19     04/27     Homotopy and path homotopy     Lect 19     PSet 10, part 1   : Due May 09.
  Lecture 20     05/04     The fundamental group     Lect 20     PSet 10, part 2   : Due May 09.
  Lecture 21     05/09     The fundamental groups of $S^n$ ($n \ge 1$) and applications     Lect 21     PSet 11, part 1   : Due May 16.
  Lecture 22     05/11     Van Kampen's theorem     Lect 22     PSet 11, part 2   : Due May 16.
  Lecture 23     05/16     Covering spaces     Lect 23     PSet 12, part 1   : Due May 23.
  Lecture 24     05/18     The classification of covering spaces     Lect 24     PSet 12, part 2   : Due May 23.
  Lecture 25     05/23     Brouwer's fixed point theorem; Brouwer's invariance of domain theorem     Lect 25     PSet 13, part 1   : Due May 30.
  Lecture 26     05/25     Jordan curve theorem     Lect 26     PSet 13, part 2   : Due May 30.
  Lecture 27     05/30     Classification of curves; Knots and links     Lect 27     PSet 14, part 1   : Due June 08.
  Lecture 28     06/01     Topology of compact surfaces     Lect 28-29     PSet 14, part 2   : Due June 08.
  Lecture 29     06/06     Classification of compact surfaces     PSet 14, part 3   : Due June 08.
      06/08     Problem Session by TA        
      06/21     Final Exam: Cover Lecture 1-Lecutre 29, 8:30-10:30 @ 2103      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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