Fall 2021 MATH 5404
Topology 拓樸學
Syllabus 課程大綱
宣導事項
- 9/17/2021: Welcome to the class!
教學進度
9/17/2021(星期五): Introduction to topology.
9/21/2021(星期二): No Class (中秋節連假).
9/24/2021(星期五): Quick review of set and logics.
9/28/2021(星期二): Introduction to metric spaces.
10/1/2021(星期五): Open and closed subset.
10/5/2021(星期二): Interior and closures, complete metric spaces.
10/8/2021(星期五): Baire category theory.
10/12/2021(星期二): The real line and product metric spaces.
10/15/2021(星期五): Product metric spaces.
10/19/2021(星期二): Compact metric spaces.
10/21/2021(星期五): Compact metric spaces.
10/26/2021(星期二): Continuous functions.
11/2/2021(星期二): Midterm 1.
11/5/2021(星期五): Introduction to topological spaces.
11/9/2021(星期二): Subspaces and continuity.
11/12/2021(星期五): Base of topology.
11/16/2021(星期二): Bases of topology, separataion axioms.
11/19/2021(星期五): Urysohn's lemma.
11/23/2021(星期二): Uniform Cauchy and convergence, Tieze extension theorem.
11/26/2021(星期五): Compactness in topological spaces.
11/30/2021(星期二): Local compactness and one point compactification.
12/3/2021(星期五): One point compactfication.
12/7/2021(星期二): One point compactification of R^n, connectedness.
12/10/2021(星期五): Connectedness.
12/14/2021(星期二): Path connectedness, finite product spaces.
12/17/2021(星期五): Tychonoff's theorem.
12/21/2021(星期二): Midterm Exam 2.
12/24/2021(星期五): Paths and homotopy.
12/28/2021(星期二): Operations on paths, fundamental groups, induced homomorphisms.
1/4/2022(星期二): Covering spaces and lifting properties.
1/7/2022(星期五): Fundamental group of S^1, applications.
作業
Homework 1 (截止日 10/5/2021 In class):
Section 1.1: 2-8, 10-14.
Homework 2 (截止日 10/19/2021 In class):
Section 1.2: 6, 7, 8.
Section 1.3: 1, 2, 4, 5, 7.
Homework 3 (截止日 11/2/2021 In class):
Section 1.4: 4, 6, 7.
Section 1.5: 1-5, 8.
Homework 5 (截止日 12/10/2021 In class):
Section 2.5: 1, 2, 5, 6, 9.
Section 2.6: 3, 6, 8, 10.
Section 2.7: 1, 3, 4, 6.
Section 2.8: 4, 5, 6, 9, 13, 14.
Homework 6 (截止日 12/24/2021 In class):
Section 2.9: 2, 7, 8.
Seciton 2.10: 6, 4.
考試相關
Exam 1 Info.
Exam 3 Info.
講義