MA3002 — General Topology (Generell Topologi)

Revision questions
Lecture notes and exercises
Reference group
Contact Details


I have now finished grading the exams. I am happy with the results, and feel that you have all learnt a lot of topology, and done exceedingly well! Congratulations!

Here is a brief report on the exam, which includes more details on the grades. pdf


Exam. pdf

Outline solutions. pdf

A few minor errors have been corrected in this copy of the exam, and minor clarifications added, for the benefit of future students.


Spring 2014.


Now over!

Exercise/Revision classes

Now over!



This document lists all the examinable material for this year, with references.

Revision questions

Revision Question 1, 30/04. pdf Solutions and Discussion 1. pdf
Revision Question 2, 01/05. pdf Solutions and Discussion 2. pdf
Revision Question 3, 02/05. pdf Solutions and Discussion 3 (partial). pdf
Revision Question 4, 03/05. pdf Solutions and Discussion 4. pdf
Revision Question 5, 04/05. pdf
Revision Question 6, 05/05. pdf
Revision Question 7, 06/05. pdf
Revision Question 8, 07/05. pdf
Revision Question 9, 08/05. pdf
Revision Question 10, 09/05. pdf

Revision Questions 1-10 and Solutions and Discussion 1-4, all together. pdf

All of the parts of these questions could have appeared on the exam, but some are quite challenging. Don't give up if you find quite a few difficult: see this instead as a point of departure for looking up relevant material in the lecture notes; reading carefully my solutions when they appear; and if this does not help, for getting in touch with me.

I also recommend having a go at last year's exam as part of your revision.

Lecture notes and exercises

Introduction (scan of a student's notes), 06/01. pdf
Lecture 1, 06/01. pdf
Lecture 2, 07/01. pdf
Lecture 3, 13/01. pdf
Lecture 4, 14/01. pdf
Lecture 5, 20/01. pdf
Lecture 6, 21/01. pdf
Lecture 7, 27/01. pdf
Lecture 8, 28/01. pdf
Lecture 9, 03/02. pdf
Lecture 10, 04/02. pdf
Lecture 11, 10/02. pdf
Lecture 12, 11/02. pdf
Lecture 13 (partial), 17/02. pdf
Lecture 14, 18/02. pdf
Supplementary document on the classification of surfaces. pdf

Lectures 1-14, together. pdf

The source files can be found at the git repository for the lecture notes.

Reference group

Åsmund S Folkestad, Joakim Gåsøy, Tjerand A Silde, and August P B Sonne represented you. Thank you to all four of you for an excellent job!


A blog was set up for the course, to get help beyond the exercise classes, and to discuss the course with each other. More details on the purpose of the blog can be found in this post.


Topology is the study of topological spaces, which are of indispensable importance across mathematics, and are equally important in physics, computer science, and other disciplines.

If the idea of studying knots, the Möbius band, the Klein bottle, or turning a sphere inside out intrigues you, or if you are baffled as to how a hundred year old problem proven recently can be of a completely different flavour in three and four dimensions than in five or more, this course is where you should start!

If you have enjoyed courses in analysis, geometry, or algebra, or any combination of these, it's likely that you'll find something to your taste in topology — it's a rich and diverse subject, and further study can lead in any or all of these directions.

This course will have two goals:

  1. To introduce examples of topological spaces, illustrating various phenomena, and conveying something of topology's geometric flavour.
  2. To develop the foundations of topology relied upon in higher courses.

Upon successful completion of the course, you will have acquired knowledge which will open up doors to higher courses, and will have developed skills — the suppleness of mind needed to understand topological pheneomena intuitively; an ability to reason at a more abstract level than you have probably come across before; the organisation and discipline necessary to match topological intuition to abstract rigour — which will be valuable to you in your chosen career.


The lectures will be given in English.

The official course description can be found here.

There are no specific pre-requisite courses. If you have any questions as to whether your background is sufficient to follow the course, please do not hesitate to get in touch.

Do not be put off by the list of recommended previous courses in the official course description: it is highly inaccurate for the course that I will give! In particular, absolutely no knowledge of linear algebra, differential equations, or complex analysis is needed.


There is no obligatory textbook. The examination will be based upon the lectures.

Detailed lecture notes will be posted as the course proceeds.

You can find lecture notes from last year here. I will make a few amendments here and there this year, but the course will be very similar.

There are many other textbooks which you may find helpful. Here is a brief list. I have ordered a few copies of Basic Topology by M.A.Armstrong for the bookshop.

Contact Details

You are welcome to contact me by email, or to come to my office at any time, to discuss anything from the lectures that you did not follow, or anything else.

My email address and office can be found here.

Last updated at 16:55 (GMT+2), 04/09/2014.