Math 145B, Introduction to Topology II

Spring 2009

MWF 11:10-12:00, Sproul 2343

Monday, March 31: Review of basic definitions from last quarter; open covers and compactness

Wednesday, April 1: Theorems about compactness

Homework: Section 26 #3, 5, 6 (due Friday, April 3)

Friday, April 3: Compactness of closed intervals on the real line

Monday, April 6: More theorems on compactness

Homework: Section 26 #12 (If you use the hint, be sure to prove it!) (due Friday, April 10)

Wednesday, April 7: Still more theorems on compactness

Homework: Section 26 #7 (due Friday, April 10)

Friday, April 9: Examples of compact spaces

Monday, April 13: Compact metric spaces

Homework: Section 27, #2 (due Friday, April 17)

Wednesday, April 15: Compact metric spaces and the uncountability of the reals

Homework: Section 27, #6 (** now due Friday, April 24**)

Friday, April 17: Other notions of compactness

Homework: Section 20, #3a (due Friday, April 24)

Monday, April 20: More on other notions of compactness

Wednesday, April 22: Locally compact spaces

Homework: Section 28 #6 (due Friday, May 1)

Friday, April 24: Locally compact spaces and one-point compactifications

Monday, April 27: Theorems about locally compact spaces

Homework: Section 29 #5, 6 (due Friday, May 1)

Wednesday, April 29: More on local compactness

Friday, May 1: Review

Monday, May 4: Midterm exam

Wednesday, May 6: Identification spaces

Homework (due Friday, May 8)

Friday, May 8: Identification maps

Homework (due Friday, May 15)

Monday, May 11: More on identification spaces

Wednesday, May 13: Projective spaces

Homework (due Friday, May 22)

Friday, May 15: Homotopies of maps

Monday, May 18: More on homotopies of maps

Wednesday, May 20: Nullhomotopic maps and homotopy equivalences

Homework (due Friday, May 29)

Friday, May 22: Deformation retractions and contractible spaces

Homework (due Friday May 29)

Wednesday, May 27: Simplicial complexes

Friday, May 29: More on simplicial complexes

Monday, June 1: Classification of closed surfaces