## Syllabus for Math 535, Section G1 Fall 2020 General Topology Under construction!

Textbooks: No textbook is required. The following books are recommended.
• General Topology by S. Willard (there is a Dover paperback and various electronic versions). A well-regarded and somewhat dated text.
• I personally don't like Topology by J. Munkres (any edition), but you may find it useful. It's not cheap either.
• Topology and Geometry by 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. No late homework will be accepted. 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.
• Exams: There will be one midterm and a final. A midterm exam will be closed book and will be administered by CBTF on Zoom.

The midterm is scheduled to take place online on 10/09/2020 12pm-12:50 pm Central time (plus 10 minutes to scan and upload); the date is not likely to change.

The final, according to the non-combined final examination schedule is to take place on 1:30 pm-4:30 pm Thursday, December 17

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. This said, I strongly recommend studying for the final no matter how well you are doing on the midterms and the homeworks.

• Content: Definition and examples of metric and topological spaces, continuous maps, bases, subbases; subspaces, products; quotient topology; nets and convergence, compactness, 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; categories, functors and natural transformations; fundamental groupoids and covering spaces.