MATH3070 - Introduction to Topology - 2016/17

Announcement

• Test 1: Feb 16 (Thu), 14:30-16:15 at ERB803 only, i.e., for all students
• Test 2: Mar 23 (Thu), 14:30-16:15 at ERB803 only, i.e., for all students

General Information

Teaching Assistant

• Wing Kit NG

Time and Venue

• Lecture: Tue 14:30-16:15 LSB LT3; Thu 15:30-16:15 MMW 702
• Tutorial: Thu 14:30-15:15 MMW 702

Pre-class Notes

• Course Description
• Prep-exercises: set language
• Prep-exercises: analysis
• Prep-Notes: metric space

Lecture Notes

• Lecture Jan 10: Definition of Topology
• Lecture Jan 12: Open sets and Nbhds
• Lecture Jan 17: Closed sets and Subbase
• Lecture Jan 19: Base
• Lecture Jan 24: Countable Base and Continuity
• Lecture Jan 26: Continuity again
• Lecture Feb 07: Subspace topology
• Lecture Feb 09: Convergence and continuity
• Lecture Feb 14: Tietz Extension
• Lecture Feb 21: Existence Extension
• Lecture Feb 23: Category and Finite Product
• Lecture Feb 27: Product Space
• Lecture March 2: Product vs Box
• Lecture March 7: Quotient Topology
• Lecture March 9: Identification Spaces
• Lecture March 14: More Quotient Examples
• Lecture March 16: Compactness
• Lecture March 21: Properties of Compact
• Lecture March 28: Compact Hausdorff
• Lecture March 30: Compactification
• Lecture April 06: Connectedness
• Lecture April 11: More connectedness
• Lecture April 13: Topological invariant
• Lecture April 18: Fundamental Group

Assignments

• Exercise 01: Topology
• Exercise 02: Open and Closed sets
• Exercise 03: Base and Countability
• Exercise 04: Continuity
• Exercise 05: Convergence
• Exercise 06: Completeness and Baire Category
• Exercise 07: Products
• Exercise 08: Quotients
• Exercise 09: Compact Properties
• Exercise 10: Compact Hausdorff
• Exercise 11: Connectedness
• Exercise 12: Homotopy
• Exercise 13: Fundamental Group