Math 145A, Introduction to Topology

Winter 2011

MWF 8:10-9:00 am, SPR 2340

 

Course Information

Monday, January 3: Set theory review

          Homework 1: Ex. 2.1, 2.3, and 2.4 in Sutherland (due Wednesday, January 5)

Wednesday, January 5: Images and inverse images of functions

          Homework: Ex. 3.1 and 3.3 in Sutherland (due Wednesday, January 12)

Friday, January 7: Invertible functions

          Homework: Ex. 2.7 and 3.10, plus problems given in class (due Wednesday, January 12)

Monday, January 10: Properties of real numbers and sequences

Wednesday, January 12: Limits and continuity of real functions

          Homework: Ex. 4.1, 4.2, 4.4, and 4.12 (due Wednesday, January 19)

          Corrections to Homework 1 can be turned in Friday

Friday, January 14: Intro to metric spaces

          Corrections to Homework 2 can be turned in Wednesday

Monday, January 17: No class – Martin Luther King Holiday

Wednesday, January 19: More examples of metric spaces

          Homework: Ex. 5.3 and 5.4 (due Wednesday, January 26)

Friday, January 21: Products of metric spaces and continuity in metric spaces

          Corrections to Homework 3 can be turned in Monday

Monday, January 24: Bounded subsets of metric spaces

          Homework: Ex. 5.7 (due Wednesday, January 26)

Wednesday, January 26: Open balls and open sets

          Homework: Ex. 5.5 and 5.13 (due Wednesday, February 2)

Friday, January 28: Open set formulation of continuity

          Corrections to Homework 4 can be turned in Monday

Monday, January 31: Closed sets

          Homework: Ex. 6.3, 6.5, 6.12 (due Wednesday, February 9)

Wednesday, February 2: Exam 1

Friday, February 4: Closure of a subset

          Corrections to Homework 5 can be turned in Monday

          Homework: Ex. 6.13 and 6.15 (due Wednesday, February 9)

Monday, February 7: Interior of a subset

Wednesday, February 9: Topological spaces

          Corrections to Exam 1 must be turned in Friday (not optional!)

          Homework: Ex. 6.23, 7.1, and 7.2 (due Wednesday, February 16)

Friday, February 11: Continuous functions of topological spaces

          Corrections to Homework 6 can be turned in Monday

          Homework: Ex. 7.6 and 8.1 (due Wednesday, February 16)

Monday, February 14: Homeomorphisms and bases

          Homework: Ex. 8.6 (due Wednesday, February 16)

Wednesday, February 16: Closure, interior, and boundary for topological spaces

          Homework: Ex. 9.4, 9.8, 9.10, 9.11, 9.12 (due Wednesday, February 23)

Friday, February 18: Review

          Corrections to Homework 7 can be turned in Wednesday (or before)

Monday, February 21: No class – President’s Day Holiday

Wednesday, February 23: Exam 2

Friday, February 25: Subspaces

          Corrections to Homework 8 can be turned in Monday

          Homework: Ex. 10.1, 10.4, 10.6, and 10.10 (due Wednesday, March 2)

          Corrections to Exam 2 must be turned in on Friday, March 4 (not optional!)

Monday, February 28: Product spaces

          Homework: Ex. 10.15 and 10.16 (due Wednesday, March 2)

Wednesday, March 2: Hausdorff spaces

          Homework: Ex. 10.18, 11.1, and 11.4 (a) and (b) (due Wednesday, March 9)

Friday, March 4: Connectedness

          Corrections to Homework 9 can be turned in Monday

Homework: Ex. 12.3 and 12.17

Monday, March 7: Connectedness and path-connectedness

Wednesday, March 9: Compactness

          Suggested problem: Ex. 12.1 (i)-(iii)

Friday, March 11: Compactness and the Heine-Borel Theorem

          Suggested problems: Ex. 13.1, 13.3, 13.4

Finals Week Office Hours: Monday-Thursday 3-4 pm (priority to other class on Monday and Tuesday)

Friday, March 18, 3:00-6:00 pm: Final Exam (in usual classroom)

 

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Last updated: 11 March 2011