MATH3070 - Introduction to Topology - 2017/18

Announcement

• (4/2/2018) Please note that Ex1)Q9) has been updated.
• (4/5/2018) Note that there is a modification in Tutorial Classwork 8. The space Y should be connected. Nonetheless, the suggested solution is correct.

---

General Information

Lecturer

• Thomas Kwok Keung AU
  • Office: LSB 213
  • Tel: 3943 7981
  • Email:

Teaching Assistant

• Ka Ho WONG
  • Office: LSB 228
  • Tel: 3943 7956
  • Email:
  • Office Hours: By appointment

Time and Venue

• Lecture: M9-10, MMW 702; W8, LPN LT
• Tutorial: W7, LPN LT

Course Description

This course is to introduce the basic notions of topology. Emphasis will be placed on providing a general foundation for learning analysis (real and functional) and geometry (algebraic and differential). The former is customarily called point set topology while the latter algebraic topology. Roughly, 80% of the course deals with entrance concepts and foundational materials for analysis; the remaining 20% leads to topological recognition of geometric space. There will be examples from Euclidean spaces, function spaces, and geometric spaces.

Pre-class Notes

• Course Description
• Required Set Language
• Preliminary Analysis

Lecture Notes

• Lecture notes 1
• Lecture notes 2
• Lecture notes 3
• Lecture notes 4
• Lecture notes 5
• Lecture notes 6
• Lecture notes 7
• Lecture notes 8
• Lecture notes 9
• Lecture notes 10
• Lecture notes 11
• Lecture notes 12
• Lecture notes 13
• Lecture notes 14
• Lecture notes 15
• Lecture notes 16
• Lecture notes 17
• Lecture notes 18
• Lecture notes 19
• Lecture notes 20
• Lecture notes 21
• Lecture notes 22
• Lecture notes 23
• Lecture notes 24

Class Notes

• Remark on definition of topology

Tutorial Notes

• Tutorial Classwork 0
• Tutorial Classwork 1
• Tutorial Classwork 2
• Tutorial Classwork 3
• Tutorial Classwork 4
• Tutorial Classwork 5
• Tutorial Classwork 6
• Tutorial Classwork 7
• Tutorial Classwork 8
• Tutorial Classwork 9

Assignments

• Exercise 1 (Topology) (Updated at 4/2/2018)
• Exercise 2 (Open and Closed Sets)
• Exercise 3 (Base of Topology)
• Exercise 4a (Continuity)
• Exercise 4b (Continuous Extension)
• Exercise 5 (Convergence)
• Exercise 6 (Complete and Baire category)
• Exercise 7 (Product Topology)
• Exercise 8 (Quotient Topology)
• Exercise 9a (Compactness)
• Exercise 9b (Compact Hasedorff Space)
• Exercise 10 (Connectedness)
• Exercise 11 (Homotopy)
• Exercise 12 (Fundamental group)

Quizzes and Exams

• Suggested Solution for Quiz 1
• Suggested Solution for Quiz 2
• Summary for Quiz 1
• Summary for Quiz 2

Solutions

• Solution of Tutorial Classwork 0
• Solution of Tutorial Classwork 1
• Remark for Tutorial 1
• Solution of Tutorial Classwork 2
• Solution of Tutorial Classwork 3
• Solution of Tutorial Classwork 4
• Solution of Tutorial Classwork 5
• Solution of Tutorial Classwork 6
• Solution of Tutorial Classwork 7
• Solution of Tutorial Classwork 8
• Solution of Tutorial Classwork 9

---

Assessment Policy

Last updated: May 04, 2018 19:13:12