## Syllabus for Math 535, Section G1,  Fall 2022 General Topology

Textbooks: No textbook is required. The following books may be useful. I plan to follow my notes.
• General Topology by S. Willard (there is a Dover paperback and various electronic versions). A well-regarded and somewhat dated text.
• Topology by J. Munkres (any edition)
• Topology and Geometry by Glen E. Bredon. You can get a copy through the library It's been awhile since I looked at this book.

• Homework: Homework problems are to be assigned once a week. They are due the following week usually before midnight on Wednesdays. Late homework will be penalized. There are several reasons why I want the homework to be turned in on time. First of all, if you are not keeping up with the homework, you are not keeping up with the class, and then you may well get lost in the lectures. Secondly, it is hard to grade fairly the homework that is turned in late. The grader would have to keep careful track of the grading rubrics and so on. In short: late homework is bad for you and means more work for the grader.

If you have questions about your homework score please take it up with the grader first. If you and the grader can't resolve the issue I will step in.

If you have questions about the homework itself, please use the forum on Moodle.

• Exams: There will be one midterm and a final.

The midterm is scheduled to take place on 10/10/2022 ; the date is not likely to change. The midterm is during the regular class time.

The final, according to the non-combined final examination schedule is to take place 8am-11am on Thursday, December 15

Requests for make-up exams require a serious documentation and are (almost) never granted. Please plan accordingly. I will drop the lowest homework score.

• Grade: The formula for the course grade is roughly as follows:
• final exam = 40 %
• midterm = 20%
• homework, 40%

The formula is here to give you a sense of how you are doing in the class. The formula is not set in stone and I may deviate by a point or two in either direction. This said, I strongly recommend studying for the final no matter how well you are doing on the midterm and the homework. Failing the final is a bad idea and could make it hard to impossible for me to give you a descent grade.

• Content: Definition and examples of metric and topological spaces, continuous maps, bases, subbases; subspaces, products; quotient topology; nets and convergence, compactness, filters and convergence, Tychonoff theorem; separation axioms: Hausdorff, regular, normal...; connectedness, local connectedness, path connectedness; compactness and completeness in metric spaces; Urysohn lemma, Tietze extension; countability axioms; paracompactness and partitions of unity; metrizability; compactifications; categories, functors and natural transformations; fundamental groupoids...

The Pandemic (apparently it is still here):

Following University policy, all students are required to engage in appropriate behavior to protect the health and safety of the community. Students are also required to follow the campus COVID-19 protocols.

Please refer to the University of Illinois Urbana-Champaign's COVID-19 website for further information.