## Math 535: General (point set) topology

### Basic Information

**Instructor: **Eugene Lerman
**e-mail:** lerman at math dott uiuc dott edu
**Homepage:**
`https://faculty.math.illinois.edu/~lerman`

** Course page:**
`https://faculty.math.illinois.edu/~lerman/535/s10.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

## Texts

Recommended texts are (there is no required text):

General Topology
by S. Willard
(A Dover edition should be available from the bookstore)

Topology
by Munkres (any edition)

Topology and Geometry by Bredon

## See this link for homework
assignments, some solutions and pdf files of lectures old (Spring 06)
and new.

Last modified: Mon Feb 22 10:59:39 CST 2010