## 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/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