Fall 2021 MATH 5404
Topology 拓樸學

Syllabus 課程大綱

宣導事項

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