MA 564: Introduction to Topology
Spring 2026
Logistical Information
Location: PSY B37
Time: Tuesday and Thursday 11AM - 12:15PM
Office Hours: Monday and Tuesday 2PM-3PM, Wednesday 10:30AM-11:30AM
Instructor Information
Lecturer: Malavika Mukundan
Email: mmukunda@bu.edu
Office: CDS 307
Syllabus
This course is meant as an introduction to point set and algebraic topology. Topics to be covered include but are not limited to:
Topological spaces and continuity
Compactness and connectedness
Metrizable topological spaces
Product topology and Tychonoff's theorem
The fundamental group and van Kampen's theorem
Covering spaces and the universal cover
The main text is Munkres, James R. Topology. 2nd ed., Prentice Hall, 2000.
Grading
Homework (bi-weekly): 40%
Midterm (Mar 3): 25%
Final (May 5): 35%
Homework
There will be a homework set posted here every other Tuesday.
Please upload your homework to Blackboard as a pdf file (hand-written and scanned) before 11:55PM Eastern Time on the due date.
In case of a late assignment due to an unavoidable emergency, please submit an official letter signed by an appropriate authority (e.g. a doctor/dean) to be considered for full credit.
Without a letter, an assignment handed in within a week after its deadline will be graded with a cap of 75%. Any further delay will result in a cap of 50%.
1. Homework 1, posted on Jan 20, due Feb 3
2. Homework 2, posted on Feb 3, due Feb 17
3. Homework 3, posted on Feb 24, due Mar 10
4. Homework 4, posted on Mar 18, due Mar 31
5. Homework 5, posted on Mar 31, due Apr 14
Notes
1. Review of set theory
2. Metric spaces
3. Topological spaces
4. Closed sets, limit points
5. Continuous functions
6. Topologies from functions and more
7. Sequences
8. More on continuous functions
9. Connectedness
10. Compactness
11. Tychonoff's Theorem
12. Urysohn's Lemma
13. Homotopies
14. The fundamental group
15. Covering spaces
16. Deformation retracts and homotopy equivalences
17. Some examples of fundamental groups