18.901: Introduction to Topology (Spring 2017)

Lecturer: Thomas Walpuski (2-177)

Final Exam: Friday 2017-05-26 9am-12n in 50-340

review 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 6 - - - -
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
Midterm
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
May 15 -

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.


Course Policy