Math 535: 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/535/s11.html
- Office: 336 Illini Hall
- Office Hours:
see my calendar
- Phone: 244-9510
- Class meets: MWF 10-10:50 in
343 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
(70 %) and the final exam (30%).
Course outline
The course is an introduction to point set topology:
- 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
- metrizability
- topology on function spaces
- categories, functors and natural transformations
- fundamental groupoid
- covering spaces
Text
Recommended text (there is no required text):
Topology and Groupoids by Ronald Brown
A paperback is
available from amazon.com for $25.46; a pdf can be purchased here
for $7.48 ), book's web page is
here.
Other books that you may find useful:
General Topology
by S. Willard
(there is a Dover edition)
Topology
by Munkres (any edition)
Topology and Geometry by Bredon
See this link for homework
assignments, some solutions and pdf scans of some of my lecture notes
Last modified: Wed Jan 19 13:00:42 CST 2011