Hiro Tanaka
Location: Derrick Hall 120
Meeting Time: Tu. and Th. 2PM to 3:20PM
Office Hours for Finals: Monday 11 AM - 12:50 PM and 2 PM - 2:50 PM. Office Hours will not be held on Tuesday, Dec 10.


This class will be an introduction to the basic language necessary to study topology. Some buzz-words you can Google include: topological spaces, continuity, compactness, metric spaces, connectedness, and Hausdorffness. (For a more official description, you can consult the university catalogue.)

Beyond a fluency with the above topics, another goal of this class is for you to become familiar with mathematical thinking---questioning and understanding why definitions exist, identifying when you or another communicator is being precise or imprecise (and for what purpose), developing tastes that are rooted in practice and informed experience, exploring the mathematical landscape on your own.

Prerequisite: MATH 3330 or MATH 3380 with a grade of C or higher.

1. Tu Aug 27: Definition of topological space, continuity of functions on the real line, definition of metric space, continuous functions for metric spaces.
2. Th Aug 29: Examples of metrics on R^n (standard, discrete, taxicab, l-infinity)
3. Tu Sep 03: Continuity between various metrics on R^n
4. Th Sep 05: Continuity and open sets
5. Tu Sep 10 (Hiro not in class): More practice with metrics on R^n
6. Th Sep 12 (Hiro not in class): Convergent sequences
7. Tu Sep 17: Are all spaces metric spaces? Open sets, and beyond metric spaces.
8. Th Sep 19: Topological spaces and metric spaces compared; product and subset topologies.
9. Tu Sep 24: Equivalence relations.
10. Th Sep 26: Coproducts and more examples of spaces. Quotient spaces.
11. Tu Oct 1: Surjections and equivalence relations
12. Th Oct 3: Exploring RP2
13. Tu Oct 8: Paper mache
14. Th Oct 10: An atlas for RP2
15. Tu Oct 15 Review session (Exam next time)
16. Tu Oct 22: Closed subsets and open covers. A bonus on Mobius strip inside RP2
17. Th Oct 24: Subcovers
18. Tu Oct 29: Closed subsets defined by polynomials, Heine-Borel
19. Th Oct 31: Closed balls, Heine-Borel
20. Tu Nov 5: Compactness. Proof of Heine-Borel.
    Also, proofs of all the propositions (and selected exercises) so far.
21. Th Nov 7: Connectedness and path-connectedness.
22. Tu Nov 12: Topologist's sine curve.
23. Th Nov 14: Closures and interiors.
24. Tu Nov 19: One-point compactifications.
25. Th Nov 21: Density and interiors.
26. Tu Nov 26: Some fun examples.

1. Writing assignment 1. Due Thursday, August 29. Homework 1. Due Tuesday, September 3.
2. Writing assignment 2. Due Thursday, September 5. Homework 2. Due Tuesday, September 10.
3. Writing assignment 3. Due Thursday, September 12. Homework 3. Due Tuesday, September 17.
4. Writing assignment 4. Due Thursday, September 19. Homework 4. Due Tuesday, September 24. Submit Multiple Choice Responses here by 1:50 PM Tuesday.
5. Writing assignment 5. Due Thursday, September 26. Homework 5. Due Tuesday, October 1. Submit Multiple Choice Responses here by 1:50 PM Tuesday.
6. Homework 6 to be submitted on TRACS by 1:50 PM Tuesday, October 8. There is no multiple choice, and no writing assignment.
7. Homework 7 to be submitted on TRACS by 1:50 PM Tuesday, October 15. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is no writing assignment this week.
8. Homework 8 to be submitted on TRACS by 1:50 PM Tuesday, October 29. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class (so print it out).
9. Homework 9 to be submitted in person Tuesday, November 5. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class (so print it out).
10. Homework 10 to be submitted in person Tuesday, November 12. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class.
11. Homework 11 to be submitted in person Tuesday, November 19. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class.
12. Homework 12 to be submitted in person Tuesday, November 26. Submit Multiple Choice Responses here by 1:50 PM Tuesday. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class.
13. Homework 13 to be submitted in person Tuesday, December 3. No Multiple Choice questions. There is a writing assignment this week which you can find in the PDF of the homework; it is also due on Tuesday, in person in class.

Extra credit, due Thursday, December 5th.

1. Solutions to HW 1
2. Solutions to HW 2
3. Solutions to HW 3
4. Solutions to HW 4
5. Solutions to HW 5
6. Solutions to HW 6
7. Solutions to HW 7
8. Solutions to HW 8
9. Solutions to HW 9
10. Solutions to HW 10
11. Solutions to HW 11
12. Solutions to HW 12

1. Metric spaces. Here are the solutions.

There will be no textbook that we follow in this class. However, I do recommend Allen Hatcher's notes on point-set topology.