Lecturer: Thomas Walpuski (2-177)
Final Exam: Friday 2017-05-26 9am-12n in 50-340review notes
|Week starting||Topics||Reading||Problem Set||Seminar Speaker(s)|
|February 6||Logic and set theory||Chapter 1|
|February 13||Logic and set theory (cont.) + What is a topological space?||
partial lecture notes
Sections 12, 14, 16
|Problem Set 1||Maria Ivan and Diego Roque|
|February 20||What is a topological space?||Sections 13, 20, 21||-||-|
|February 27||Interior, closure and boundary; continuous maps; disjoint unions||remaining sections of Chapter 2||Problem Set 2||Jacob Martin and Hui Xu|
|March 13||quotients, products; connectedness, path connectedness; compactness||Sections 19, 22, 23, 24, 25, 26||Problem Set 3||José Alan Esparza and Luna Gonzalez|
|March 20||compactness; sequences and countablity axioms||Sections 26, 27, 30
sequential compactness in metric spaces
|Problem Set 4||Calvin Hsu and Sanzeed Anwar|
|March 27||Spring Vacation|
|April 3||proof of Tychonoff's theorem||Section 37;
a curious proof that RR is not metrizable;
notes on the proof Tychonoff's theorem
|April 10||one-point compactification; Urysohn's Lemma; Tietze's Extension Theorem||Sections 29; 32; 33; 35||Problem Set 5||Jingwen Chen and Robert Kao|
|April 17||Urysohn's Metrization Theorem||Sections 34, 35||Problem Set 6||Magdalen Dobson and Rikhav Shah|
|April 24||Compact-open topology; homotopy, homotopy-equivalence||Sections 46, 51, 58||Problem Set 7||Haimei Zhang and Justin Lim|
|May 1||The fundamental group; computation for the circle; applications||Sections 52, 54, 55, 56||Problem Set 8||Bertrand Stone and Rong Li|
|May 8||Covering spaces||Problem Set 9||Alexander Moss and Kuo-An Wei|
The text book for this class is Munkres' Topology and I will assign reading to you every week to solidify the material I teach in class. I also recommend the Counterexamples in Topology to browse on the subway or as night-time reading.
There is going to be a final exam and one midterm.
We will have problem seminar almost every week during the lecture on Thursday. A group of two of the students will present their solution to the last problem of the problem set. If you want to volunteer for the seminar, email me, ask me afterclass or just drop by my office.
There are not going to be typed lecture notes for the entire class. I do encourage you to take notes in the class.