MATH 535: General Topology (Fall 2017)

Course meets

TR 1:30–2:50 p.m. in 207 Psychology Lab.

Instructor: James Pascaleff

Email: jpascale@illinois.edu
Office: 341B Illini Hall
Office hours: W 3:00–5:00 p.m.

Prerequisites

None (logically speaking). If you are concerned whether this course is right for you, please contact the instructor by e-mail.

Recommended Text

Topology by J.R. Munkres.

Exams

Midterm exam: October 12, in class.
Final exam: Saturday, December 16, 8:00–11:00 AM, 207 Psychology Lab.

Follow this link for the detailed schedule including topics, lecture notes, and homework.

You can view your homework scores by following this link.

Date and Time

Thursday, October 12, usual time and room.

Topics

This midterm will cover the course up to lecture 10, or the first three homework assignments.

Format

The midterm will consist of free-response problems. There will be a list of problems, and you will be asked to complete a subset of your choosing. For instance, it will say something like "Of the following 8 problems, please complete 5 of your choosing."

Types of questions

The problems will be roughly at the level of the homework problems. Due to the time constraints, I will include problems that have relatively straightforward solutions. There may also be problems that ask you to prove a proposition that was proved in the lectures, but these will be a minority.

Office hours

Usual office hours Wednesday October 4, 3-5 pm. I will not have office hours Wednesday October 11. Instead, I will have office hours Tuesday October 10, 3-5 pm. I can also answer questions via Piazza (preferred) or email.

Homework will be due periodically throughout the semester. You should expect 10 assignments total, or approximately one assignment every one and a half weeks.

Please pay attention to the due date for each assignment. On days that homework is due, please turn in your homework in class.

The lowest homework score will be dropped. This means, for instance, that you can miss one homework without penalty.

While students are encouraged to ask questions, share ideas, and work together to solve the homework problems, each student must write up their solutions themselves in their own words.

Grades will be based on homework, the midterm exam, and the final exam, with percentages as follows:

Homework	50%
Midterm	20%
Final	30%

Homework Grader: Elliot Kaplan (eakapla2@illinois.edu)

There is a Piazza forum for this course. Students may use this forum to discuss the course material, including the homework problems. While discussion of homework problems is allowed, users of the forum should refrain from posting complete or near-complete solutions to the problems. It is appropriate, however, to post suggestions, hints, or references to the relevant parts of the textbook or lecture notes.

Use of the forum is optional. You can sign up for the forum at piazza.com/illinois/fall2017/math535. You can use any email address, making it possible to use the forum pseudonymously if you prefer.

This course is an introduction to point set topology, a foundational topic for much of modern mathematics, particularly analysis and other flavors of topology. In the last part of the course, we will also cover the fundamental group, the most basic algebraic topological invariant.

List of topics:

• Topological structures, continuous functions, basis and subbasis for a topology.
• Subspaces, products, quotients.
• Metric spaces.
• Sequences and nets.
• Separation axioms (Hausdorff et al.)
• Connectedness, compactness, Tychonoff theorem.
• Metrizability.
• Topology on function spaces.
• Fundamental group and groupoid, covering spaces.
• Categories, functors, and natural transformations.

Recommended text: Topology by J.R. Munkres.