Math 205C, Topology

Fall 2015

MWF 2:10-3 pm, Surge
284

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