Math 145A: Introduction to Topology

Winter 2012

Monday,
January 9: Set theory review

Homework: 2.1, 2.2, 2.3, 2.4 (due
Wednesday, January 11)

Wednesday, January
11: Direct and inverse images of functions

Homework: 3.1, 3.3 (due Wednesday,
January 18)

Friday,
January 13: Bounded subsets of R

Homework: 3.5, 3.6 (due Wednesday,
January 18)

Monday,
January 16: Martin Luther King, Jr Holiday

Wednesday,
January 18: Limits of sequences and functions

Homework: 4.1, 4.2, 4.4, 4.12 (due
Wednesday, January 25)

Friday,
January 20: Continuity and metric spaces

Homework: 5.3, 5.4 (due Wednesday,
January 25)

Corrections to Homework 1 and 2 can be
turned in Monday

Monday,
January 23: Examples of metric spaces

Wednesday,
January 25: Products and metric subspaces

Friday,
January 27: Bounded subsets of metric spaces

Homework: 5.7 (due Wednesday, February
1)

Monday,
January 30: Open balls and open sets

Homework: 5.6, 5.13 (due Wednesday,
February 1)

Wednesday,
February 1: Exam #1

Corrections to Homework 3 can be
turned in

Friday,
February 3: Closed sets

Homework: 6.3, 6.5, 6.12 (due
Wednesday, February 8)

Corrections to Homework 4 can be
turned in Monday

Monday,
February 6: Closure of a subset

Homework: 6.13 (due Wednesday,
February 8)

Wednesday,
February 8: Interior of a subset

Homework: 6.15, 6.20 (due Wednesday,
February 15)

Friday,
February 10: Topological spaces

Homework: 6.23, 7.1, 7.2, 7.6 (due Wednesday,
February 15)

Corrections to Homework 5 can be
turned in Monday

Monday,
February 13: Continuous functions of topological spaces

Homework: 8.1 (a) and (d) only (due
Wednesday, February 15)

Wednesday,
February 15: Closed sets in topological spaces

Homework: 8.4, 8.6, 9.4 (due
Wednesday, February 22)

Friday,
February 17: Generalizing closures, interiors, and boundaries to topological
spaces

Homework: 9.8, 9.14 (due Wednesday,
February 22)

Corrections to Homework 6 (plus
problem 6.15) can be turned in on Wednesday

Monday,
February 20: No class – President’s Day

Wednesday,
February 22: Exam #2

Friday,
February 24: Subspaces

Homework: 10.1, 10.6 (due Wednesday,
February 29)

Corrections to Homework 7 can be
turned in on Monday

Monday,
February 27: Product spaces

Homework: 10.16 (due Wednesday,
February 29)

Wednesday,
February 29: Hausdorff spaces

Homework: 10.18, 11.1, 11.4 (a) and
(b) only (due Wednesday, March 7)

**Note: 10.18 should have
f:X->X’ and g:Y->Y’**

Corrections to all of Exam 2 are due
Friday!

Friday,
March 2: Connectedness

Homework: 12.3, 12.17 (due Wednesday,
March 7)

Corrections to Homework 8 can be
turned in on Monday

Monday,
March 5: More on connectedness

Wednesday,
March 7: Path-connectedness

Homework: 12.1 (i)-(iii)
only (due Wednesday, March 14)

Friday,
March 9: Compactness

Homework: 13.1, 13.2, 13.3 (due
Wednesday, March 14)

Corrections to Homework 9 can be
turned in on Monday

Monday,
March 12: More on compactness

Homework: 13.10 (due Wednesday, March
14)

Wednesday,
March 14: Compactness of product spaces

Friday,
March 16: Wrap-up and review

Extra office hours: 3-5 pm

Monday,
March 19: Final exam 8-11 am

Last updated: 15 March 2012