MA30055 - Introduction to Topology

Introduction to Topology
Level 3

Semester 2 in 2018/19

General course information and handouts

This unit introduces the category of topological spaces and continuous maps.

Class times and locations: The lectures take place on Mondays at 10:15 (6W 1.1), Tuesdays at 10:15 (6W 1.1) and Wednesdays at 11:15 (6W 1.2).
One lecture each week (except week one) will be an examples class.

Weekly schedule and lecture notes

Topics covered each week:

Week 1: Definition of topological space, basic examples, subspaces.
Week 2: Continuous maps, category theory.
Week 3: Initial and final topologies.
Week 4: Coequalisers, subbases and bases.
Week 5: Product spaces.
Week 6: Coproducts and the Hausdorff property.
Week 7: Connectedness.
Week 8: Compactness.
Week 9: Topological surfaces.
Week 10: Classification of compact surfaces.
Week 11: Concluding the classification.

Here is the newly revised set of lecture notes for the course: lecture notes.

For completeness, the older version of the notes is here.
For reference only, here are the notes from Analysis 2A.
For those interested in a modern view of set theory that ties in well with the categorical approach used in this unit, see Tom Leinster's Rethinking set theory

Here is a link to the Panopto lectures

Office hour: My weekly office hour this semester for Introduction to Topology is Monday 13:15-14:05.

Homework assignments

Department of Mathematical Sciences,
University of Bath, Claverton Down,
Bath BA2 7AY.

Office: 4W 3.49
Phone: 01225 385327
Email: a.craw at bath dot ac dot uk

Introduction to Topology Level 3

Introduction to Topology
Level 3