| ISIS | Schedule | Important dates |
The word "topology" comes from the old Greek words "topos", meaning "place", and "logos", meaning "word".
The short answer is: Topology is the study of continuity. If you want a more elaborate answer, you can see here what the topologists themselves think topology is or consult The Mathematical Atlas for General Topology.
The main topics of this course are
We use
Here are some supplementary notes on General Topology.
Lectures Tuesday 8-10 and 13-15 in Aud 8 and Friday 11-12 in Aud 6.
| Week | Topics | Lectures | Problem Sessions |
|---|---|---|---|
| 1 | Introduction Review of metric spaces and continuous maps Topological spaces and continuous maps Hausdorff separation axiom Basis for a topology Open and closed maps, homeomorphisms Countability axioms Manifolds |
Chp 1 (which I assume
you read on your) Appendix p 347-350 Chp 2 |
A.11, A.12, A.13, A.14, A.16 |
| 2-1, 2-2, 2-3, 2-5, 2-6 | |||
| 2 | Interior, closure,
boundary. The embedding topology. Embeddings. The subspace topology. The quotient topology. Quotient maps. The product topology. Examples of manifolds. |
Chp 2 - 3 | 2-7, 2-9 (a) and (b), 2-14, 2-16 ( Correction to 2-16) |
| 2-9 (c), 2-11, 2-13, 2-15 (W) |
|||
| 3 |
The universal property of the quotient space. Examples of quotient spaces. Projective spaces. Connected spaces. | Chp 3 - 4 | 3-3, 3-6, 3-8, 3-9 |
| 2-18, 3-1 (W), 3-10, 3-11, 3-13 ( Correction to 2-18 and 3-1) |
|||
| 4 | Path-connected spaces,
locally (path) connected spaces. Compact spaces, locally compact spaces |
Chp 4 | 4-1, 4-2, 4-4, 4-5 |
| 4-7 (W), 4-10, 4-11, 4-12 | |||
| 5 | Simplicial complexes Orientation Euler characteristic |
Chp 5 | 5-1, 5-2, 5-3, 5-4 ( Corrections to 5-2, 5-3) |
| 5-6, 5-7 (W), 5-8, 5-9, 5-10 | |||
| 6 | 1- and 2-dimensional manifolds | Chp 6 | 5-12, 6-1 |
| 6-2, 6-3, 6-4 (W) January 2006 |
|||
| 7 | Classification of
compact surfaces Repetition |
Chp 6 | 2-12, 2-17, 3-2, 3-12 |
| 3-7, 3-15, 4-13 |
Problems marked with (W) are written assignments. Hand in your solution to the instructor!
There will be a three hour written exam. (According to SIS, the exam is scheduled to January 26 2007 with re-examination on April 20 2007.) The exam will cover Chp 2, 3, 4, 5, 6 in Lee's book. There will be no questions in: 4.23, 4.24, 4.32, 4.33, 4.34, 4.35, and 5.19. You may use books, notes, computer at the exam.
At the homepage for Mat 3GT you can find solutions to hundreds of exercises from Munkres' book.
| History of Topology | Henri Poincaré (1854-1912) biography
1 and
biography 2 Poul Heegaard |
| Ask a topologist | Topology Atlas |
| Introduction to topology | RECOGNIZING SURFACES |
| The Optiverse | Electronic Geometric Models |
| Thurston: The Geometry and Topology of Three-Manifolds | Conway's ZIP Proof |
| Klein Bottles for sale! | Jesper's home-page |