535, Section G1, Fall 2022
No textbook is required. The following books may be useful. I plan
to follow my notes.
Professor: Eugene Lerman
Office: 37 Computer Applications Building (CAB)
Phone: (217) 244-9510 (feel free to leave a message)
email: lerman at illinois edu
Home page: https://faculty.math.illinois.edu/~lerman
- homework assignments are on
Moodle (Moodle login help is here )
Office Hours: TBA. Check my calendar here
10:00 am - 10:50 am MWF Altgeld Hall 441
Prerequisites: None, really. But it's supposed to be a
graduate math course. If you have any questions or concerns, please contact me by e-mail.
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
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
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
final exam = 40 %
midterm = 20%
- homework, 40%
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
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.
Last modified: Sat Aug 13 12:54:56 CDT 2022