MAT 327: Introduction to Topology, Fall 2011

Instructor: Florian Herzig; my last name at math dot toronto dot edu
Office Hours: Wednesdays 10:30am-12:30pm at BA 6186

TA: Micheal Pawliuk; m dot pawliuk at utoronto dot ca

Lectures: Mondays 2-3pm, Thursdays 2-4pm at SS 1086
On Monday, Dec 5, we'll have a make-up class 3-4pm (just after the regular class time). Location: MP 118 (McLennan Physical Labs)

Class photo

Topics to be covered (rough plan)


Also recommended: Jänich Topology (for intuition and general picture), Armstrong Basic Topology (especially for last part on homotopy)

Grading scheme

Homeworks will be usually be posted on this web page on Thursdays and be due on the following Thursday (in class or by e-mail to the TA). No late homework will be accepted! Your lowest two homework scores will not count towards your grade.

The term test will be on Thu, October 27, 2-4pm. There will be no makeup test! If you miss the test for a valid reason, the grade will be reweighted as 35% homework and 65% final.

The final will be on Thu, December 15, 9am-12pm at SS 2127.


Term test


Detailed schedule and lecture notes

Thanks to Hayoon for providing lecture notes!

Day Topics Book sections Notes
9/12 introduction   pdf
9/15 topological spaces, continuous maps, bases 12, 13 pdf
9/19 more on bases, subbases 13 pdf
9/22 subspace and product topology 15, 16 pdf
9/26 order topology, closed sets, closure 14, 17 pdf
9/29 limit points, some separation axioms (Hausdorff = T2, T1), more on continuity 17, 18 pdf
10/3 more on continuity, homeomorphisms 18 pdf
10/6 product topology in general 19 pdf
10/10 (Thanksgiving, no class)    
10/13 metric topology 20, 21 pdf
10/17 connectedness 23, 24 pdf
10/20 more on connectedness, path connectedness 23, 24 pdf
10/24 compactness 26, 27 pdf
10/27 Term Test    
10/31 more on compactness 26, 27 pdf
11/3 compactness in metric spaces 27, 28, 45 pdf
11/7 (Fall break, no class)    
11/10 compactness (end), the Cantor set 27, 28, 45 pdf
11/14 separation axioms: T3, T4 31, 32 pdf
11/17 more on separation axioms, Urysohn's lemma 31, 32, 33 pdf*
11/21 Tietze extension theorem 35 pdf
11/24 Tychonoff's theorem: Micheal's notes 37 pdf
11/28 homotopy of paths 51 pdf
12/1 more on homotopy, fundamental group, case of circle (beginning) 51, 52, 53, 54 pdf*
12/5 fundamental group of circle (conclusion), Brouwer fixed point and Borsuk-Ulam 54, 55, 57 pdf

*These two PDF files only seem to work with apple's preview. Hayoon provided alternative versions: pdf pdf