Math 595: General (point set) topology
Basic Information
- Instructor: Eugene Lerman
- e-mail: lerman at math dott uiuc dott edu
- Homepage:
http://www.math.uiuc.edu/~lerman
- Course page:
http://www.math.uiuc.edu/~lerman/595/home.html
- Office: 336 Illini Hall
- Office Hours: to be announced and by appointment.
- Phone: 244-9510
- Class meets: 1-2pm in 241 Altgeld Hall
Prerequisites
None, really.
If you have any questions or concerns, please contact me by e-mail.
Grades
The course grade will be based on weekly homework
and the final exam.
Course outline
The course is an experimental version of
math 535, point set topology. It will attempt to cover the essentials
of point set topology in half the semester. It will take a
categorical perspective on the subject.
- Definition and examples of topology, topological spaces and
continuous maps, bases, subbases.
- subspaces, products
- metrics and pseudometrics
- quotient topology
- nets
- separation axioms: Hausdorff, regular, normal...
- connectedness, local connectedness, path connectedness
- compactness, Tychonoff theorem
- compactness and completeness in metric spaces
- Urysohn lemma, Tietze extension
- countability axioms
- paracompactness and partitions of unity
- topology on function spaces
Texts
Recommended texts are (there is no required text):
General Topology
by S. Willard;
Topology
by Munkres (any edition);
Topology and Geometry by Bredon
see this page for an older version of the course.
Last modified: Thu Oct 18 09:56:02 CDT 2007