Math 205C, Topology

Fall 2015

MWF 2:10-3 pm, Surge 284

Course information

Friday, September 25: Topologies and bases

Homework: Section 13 #1, 2, and 7 (due Monday, October 5)

Monday, September 28-Friday October 2: The product and subspace topologies; closed sets and limit points

Homework: Section 16 #1, 3, 4; Section 17 # 2, 6 (due Monday, October 5)

Monday, October 5: Hausdorff spaces and continuity

Homework: Section 17 #11, 19 and Section 18 #1, 2 (due Monday, October 12)

Wednesday, October 7: Homeomorphisms and continuity results

Homework: Section 18 #4, 9, 10, 13

Friday, October 9: Infinite product spaces

Homework: Section 19 #5

Monday, October 12: Metric topology

Homework: Section 20 #3, Section 21 #1,2

Wednesday, October 14: Quotient spaces

Homework: Section 22 #2, 5

Friday, October 16: More on quotient spaces

Monday, October 19: Connectedness

Homework: Section 23 #2, 5

Wednesday, October 21: Path connectedness and local (path) connectedness

Homework: Section 24 #8 and Section 25 #8

Friday, October 23: Compactness

Homework: Section 26 #3, 5, 6 (due Monday, November 2)

Monday, October 26: More about compactness

Wednesday, October 28: Variants of compactness

Homework: Section 27 #6, Section 29 #5, 6

Friday, October 30: One-point compactifications

Monday, November 2: Midterm exam

Wednesday, November 4: Homotopy and path homotopy

Homework: Section 51 #1-3

Friday, November 6: Fundamental group

Homework: Section 52 #2, 4, 6 (due Monday, November 16)

Monday, November 9: Covering spaces

Homework: Section 53 #3, 4

Wednesday, November 11: Veterans Day Holiday

Friday, November 13: Path and homotopy lifting

Monday, November 16: Fundamental group of the circle

Homework: Section 54 #7, 8

Wednesday, November 18: Retractions and fixed points

Homework: Section 55 #1, 2

Friday, November 20: Homotopy types of spaces

Monday, November 23: Some computations of fundamental groups

Homework: Section 58 #4, 5, Section 60 #1, 4

Wednesday, November 25: Seifert-van Kampen Theorem

Homework: Section 71 #3

Friday, November 27: No class Happy Thanksgiving!

Monday, November 30: Computations of fundamental groups

Wednesday, December 2: Borsuk-Ulam Theorem

Suggested problems: Section 73 #1, Section 57 #1, 2

Friday, December 4: Assorted topics/wrap-up

Final Exam: Thursday, December 10, 4-7 pm


Last updated: 4 December 2015