MATH 535 - General Topology
Fall 2013
A topologist is someone who cannot tell the difference between a coffee mug and a donut.  Or bagel, in this case.

A printable syllabus can be found here. A note regarding emergency procedures in the case of fire, tornado, or an active threat can be found here. (It can also be found on the syllabus.)

Course Information

  • Section: MATH 535 Section X1
  • Time: MWF 12:00-12:50pm
  • Location: 443 Altgeld Hall
  • Instructor: Jordan Watts
  • Email: jawatts at illinois
  • Office Hours: W 11-12 (with the condition that I may be late), W 4-5, or by appointment
  • Office: 238 Illini Hall

Course Description

This course is an introduction to point set topology. We will (try to) cover the following topics:

  • definitions and examples of topological spaces and continuous maps,
  • bases and subbases,
  • subspaces, products, and quotients,
  • metrics and pseudometrics,
  • nets,
  • separation axioms: Hausdorff, regular, normal, etc.,
  • connectedness, local connectedness, path connectedness,
  • compactness, Tychonoff's theorem,
  • Urysohn's Lemma, Tietze's Extension Theorem,
  • countability axioms,
  • paracompactness and partitions of unity,
  • metrisability,
  • topology on function spaces,
  • categories, functors, and natural transformations,
  • the fundamental groupoid, covering spaces

Prerequisites and Restrictions

4 credit hours. MATH 444, 447, or equivalent, or consent of instructor. Basically, you should know and be comfortable with what open and closed sets are in Euclidean space, as well as continuous functions, sequences, limits, etc.


There will be no required text for MATH 535. The recommended text will be Topology and Groupoids by Robert Brown, 2006 edition, BookSurge Publishing. There is a webpage for the book here, and a cheaper digital version can be found here.

Other potentially useful books include:

  • General Topology by S. Willard
  • Topology by Munkres
  • Topology and Geometry by Bredon


There will be a final exam worth 30% of the course grade. The remaining 70% will be based on homework assignments. There will be 13 weekly homework assignments, of which the best 10 will count toward your final grade. Each homework will be due at the beginning of class on Fridays. LATE HOMEWORK WILL NOT BE ACCEPTED. Also, while you are encouraged to work together, your assignments are expected to be in your own words. Copying of any kind is considered an academic offence and will be dealt with accordingly. Finally, if your final exam average is better than your homework average (after dropping the lowest three), then your grade will be reweighted: the final will be worth 40% and the homeworks 60%.