Math 145A: Introduction to Topology

Winter 2012

 

Course Information

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