# Math 551, Elementary Topology - Fall 2009

# Nigel Boston

## Contact Information

303 Van Vleck, 3619 Engineering Hall
Telephone: 263-4753, 265-3817.

E-mail: *boston@math.wisc.edu*

Homepage

Office Hours: 3:30-5 Tues, 303 Van Vleck; 11-12:30 Weds, 3619 Engineering Hall; or by appointment.

## Text

James R. Munkres, Topology (2nd Edition).
## Lecture Outline

- Sept 3: Overview of course. Section 1.
- Sept 8: Sections 2 and 3.
- Sept 10: Rest of section 3. Sections 4 and 5.
- Sept 15: Section 6.
- Sept 17: Section 7 plus other results on uncountability.
- Sept 22: Chapter 2, section 12 and part of section 13.
- Sept 24: The rest of section 13.
- Sept 29: Sections 14, 15, and 16.
- Oct 1: Go over 1st HW, some more of section 16.
- Oct 6: The rest of section 16 and most of section 17.
- Oct 8: The rest of section 17.
- Oct 13: Most of section 18.
- Oct 15: Go over 2nd HW, finish section 18.
- Oct 20: Section 19 and start section 20.
- Oct 22: Review for 1st Midterm.
- Oct 27: 1st Midterm.
- Oct 29: Went over 3rd HW plus more of section 20.
- Nov 3: Returned 1st Midterm, went over solutions, finished section 20, and started 21.
- Nov 5: Section 21.
- Nov 10: Section 23.
- Nov 12: Go over 4th HW.
- Nov 17: Section 24.
- Nov 19: Section 26.
- Nov 24: Section 27.
- Dec 1: Go over 5th HW and review for 2nd Midterm.
- Dec 3: 2nd Midterm.

## Sections

- Main Lecture: TR 1:00-2:15, B123 Van Vleck.

## Course Description

- Elementary Set Theory: Sets, Cartesian products, equivalence relations, countability, the real line
- Basic Topology: metric spaces, topological spaces, basis, continuity, connectedness, compactness
- Selected Topics (time permitting): Product and quotient topologies, manifolds, normality and extension theorems, the fundamental group, covering spaces

## Homework Assignments

Homework will be set every other Thursday and due two weeks later. You are encouraged to discuss
the exercises with your classmates but the work you hand in should be your own. You will be
expected to read the sections of the book to be covered in advance of class.

- HW1: Due Thursday, Sept 24. 1: 1,3. 2: 2. 3: 3,4,15. 4: 10. 5: 4(d)(e)(f). 6: 3. 7: 4.
- HW2: Due Thursday, Oct 8. 13: 1, 3, 4, 5. 16: 1, 3, 4, 6. 17: 2, 3.
- HW3: Due Thursday, Oct 22. 17: 6, 9, 12, 13. 18: 3, 5, 6, 11, 12. 19: 7.
- HW4: Due Thursday, Nov 5. 19: 8. 20: 2, 3, 4, 9, 10. 21: 2, 6.
- HW5: Due Thursday, Nov 19. 21: 7, 12. 23: 5, 9, 11. 24: 1, 2, 3.
- HW6: Due Tuesday, Dec 8. 24: 9, 11. 26: 3, 5, 6, 7. 27: 2, 4.

## Midterms

Tues, Oct 27, in class.
Thurs, Dec 3, in class.

## Final Exam

10:05am-12:05pm, Friday, Dec 18, B115 Van Vleck.

## Grading Policy

Midterms 20% each, HWs 20% (lowest dropped), final exam 40%.