MA323 - Topology, Fall 2020

• Final exam on Friday, Jan. 8: Secs. 51-55, 58-60; Secs. 23-29, 30-36; Secs. 12-22, 1-7, 9 & 10.

• Here are solutions to the midterm exam.

• Assignment 13 (required, not collected): Sec. 53 #4, 5; Sec. 54 #7, 8; Sec. 55 #1, 2; Sec. 58 #5, 9; to be continued.

• Examples of covering maps in nature: 1, 2.

• Assignment 12 due Tuesday, Dec. 15: Sec. 51 #2, 3; Sec. 52 #2, 3, 4, 6, 7; Sec. 53 #3.

• Assignment 11 due Tuesday, Dec. 8: Sec. 33 #8; Sec. 34 #7; Sec. 36 #4, 5.

• Assignment 10 due Tuesday, Dec. 1: Sec. 30 #1, 4; Sec. 31 #5, 6; Sec. 32 #1, 6; Sec. 33 #3; Sec. 35 #1, 2 (optional), 4, 7.

• Assignment 9 due Tuesday, Nov. 24: Sec. 27 #5, 6; Sec. 28 #7, [Food for thought: Is the unit sphere in ℝ^ω, equipped with the product topology (cf. Theorem 20.5), compact? Is it sequentially compact (Riesz's lemma may be relevant)? Is it contained in an infinite product of finite closed intervals (which is compact by Tychonoff's theorem)?]; Sec. 29 #6, 7, 9; Supplementary exercises on nets (optional, sometimes used in real analysis).

• Assignment 8 due Tuesday, Nov. 17: Sec. 26 #1, 2, 7, 8, 13.

• Assignment 7 due Tuesday, Nov. 10: Sec. 23 #5, 10; Sec. 24 #1, 3, 9; Sec. 25 #7, 9.

• Midterm exam on Tuesday, Nov. 3: Secs. 12-22, 1-7, 9 & 10.

• Here are supplementary notes for universal properties. You should not read them unless you really want to.

• Assignment 6 due Tuesday, Oct. 27: Sec. 20 #10; Sec. 21 #2, 3; Sec. 22 #2.

• Assignment 5 due Tuesday, Oct. 20: Sec. 18 #1, 2, 10; Sec. 19 #6, 7; Sec. 20 #3, 8.

• Assignment 4 due Tuesday, Oct. 13: Sec. 17 #5, 6, 13, 15, 19.

• Assignment 3 due Tuesday, Sept. 29: Sec. 13 #3, 4, 8; read Sec. 14; Sec. 16 #9.

• Assignment 2 due Tuesday, Sept. 22: Sec. 6 #2; Sec. 7 #4, 6; Sec. 10 #3, 6, 7.

• Assignment 1 due Tuesday, Sept. 15: Sec. 1 #4; Sec. 2 #2, 4; Sec. 3 #2, 3, 13; Sec. 4 Show that the strong induction principle implies the principle of induction (we showed in class that the latter implied the former via the well-ordering property of ℤ₊); Sec. 5 #3.

Instructor

朱一飞 ZHU Yifei

Huiyuan 3-419

8801 5911

zhuyf@sustech.edu.cn

Office Hours: Monday 2:30-4:00 pm, Thursday 10:00-11:30 am

Grader: 方秋宇 FANG Qiuyu

Class QQ group: 835079431

Prerequisites

Abstract Algebra (MA214/219) or consent of the department.

Textbooks

We will be working from James R. Munkres's Topology, Second Edition.

Useful references include《基础拓扑学讲义》尤承业编著 and《点集拓扑与代数拓扑引论》包志强编著 as well as M.A. Armstrong's Basic Topology.

The textbook and the references are available at Lynn Library.

Objectives

This course introduces basic notions and examples in general topology and algebraic topology, with a view towards more advanced analysis, (algebraic and differential) geometry, and topology courses. We will cover most of Chapters 1-4, 7, 9, and 11-13 in the Munkres text.

Exams

There will be one in-class midterm exam, on November 3, and one final exam. Each of these exams is worth 30% of your final grade.

Homework

The assigned problems for each week are due each Tuesday in-class at 2 pm, listed on this page. Homework is worth 40% of your final grade. Students must make arrangements in advance if they will not be handing in homework on time.

We encourage you to discuss homework problems with your classmates, including strategies for solving different kinds of problems. However, when you actually write up your solutions, you must do this on your own.