MA3002 General Topology - Spring 2015

This is no longer a draft version of the course page. It will still be updated regularly.


What's new?

  • 17 Jul 2015: The re-exam will be oral.

What's old?

  • 5 Jun 2015: Thanks to everyone who attended the course! It was a pleasure for me, and I hope that so it was for you as well. If you are thinking about doing a topology (or other) project with me, don't hesitate to contact me (or see my webpage first).
  • 4 Jun 2015: The file exam2015.pdf has the exam problems with hints for solutions. You should have your results within a couple of days from now.
  • 24 Apr 2015: I have corrected the setup for the problems on page 6.
  • 21 Apr 2015: We will spend most of the remaining three lectures working on problems and exercises. I have added some more (page 5) to the file.
  • 9 Apr 2015: I just learnt that Onsager Professor Xiang-Yu ZHOU will give his lecture Start with complex numbers on Friday 10 Apr at 13:15 in KJL 2. I suggest that we go there after the break. The recap will continue on Tuesday 14 Apr if needed.
  • 7 Apr 2015: Added a new reference and a link to old exams for MA3002.
  • 27 Mar 2015: Next lecture on 10 April 2015 will be a recap. It's a good idea to review before and bring your questions to class.
  • 24 Mar 2015: The lecture today had to be cancelled. :-(
  • 17 Mar 2015: Put the notes for the section on nets and filters into the references.
  • 16 Mar 2015: Added some more exercises (on filters).
  • 26 Feb 2015: Added some more exercises and improved the first worksheet some more.
  • 6 Feb 2015: The worksheet now has hints for solutions on it. It also contains a remark that corrects a statement made during class.
  • 5 Feb 2015: The file with the exercises keeps growing. I have added a worksheet on sums that we will work through tomorrow in class. Make sure that you bring enough coffee.
  • 16 Jan 2015: Added more exercises and some challenges. The latter are harder than what I would expect in an exam. But, some of you might want to try them anyway.
  • 9 Jan 2015: Added exercises below.
  • 6 Jan 2015: I have been in KJL24 to check: There are only twelve tables, but probably enough chairs to sit everyone.
  • 5 Jan 2015: The first lecture will take place tomorrow as scheduled.
    To bring everyone on the same page, I will discuss metric spaces and continuous maps between them.

Course Information


  • Tuesday, 14:15 - 16:00, KJL22
  • Friday, 12:15 - 14:00, KJL24


  • Office hours: Tuesdays before the lecture in 1252, Sentralbygg II. Don't hesitate to come by and ask me.


This is the official course text:

  • J.R. Munkres. Topology. 2nd ed. Prentice Hall, 2000.

The following (parts of) books may also be useful for the purposes of the course.

  • N. Bourbaki. Topologie générale. Hermann & Cie., 1940 and later. (in French)
  • G.E. Bredon. Topology and geometry. Springer-Verlag, New York, 1993. (Chapter I and Appendix)
  • T. tom Dieck. Algebraic topology. European Mathematical Society, Zürich, 2008. (Chapter 1)
  • G. Laures, M. Szymik. Grundkurs Topologie. Spektrum Akademischer Verlag GmbH, 2009. (in German)
  • L.A. Steen, J.A. Seebach. Counterexamples in Topology. Reprint of the second (1978) edition. Dover Publications, 1995.

More references will be added here when they become relevant.


  • Part I General Topology in Munkres' book
  • Chapter 1 reviews some set theory and logic
  • Chapters 2, 3, 4 contain the core material
  • Chapters 5, 6, 7, 8 cover additional topics

(Preliminary) Lecture Plan

Week Part Topic Reading
2.1 I Happy New Year and Welcome to (General) Topology! Munkres, §20
2.2 I Metric spaces Munkres, §21
3.1 I Topological spaces Munkres, §12
3.2 I Continuous maps Munkres, §18
4.1 I Bases Munkres, §13
4.2 I Closed subsets Munkres, §17
5.1 II Subspaces Munkres, §16
5.2 II Quotients Munkres, §22
6.1 II Products Munkres, §15
6.2 II Sums Worksheet
7.1 III Connectivity Munkres, §23
7.2 III Path connectivity Munkres, §24
8.1 III Hausdorff spaces Munkres, §31
8.2 III Separated maps Worksheet
9.1 III Compact spaces Munkres, §26
9.2 III Proper maps Munkres, §27
10.1 III Compact subspaces of R Munkres, §19
10.2 no lecture on March 6
11.1 IV Nets, filters, and convergence Munkres, Supp. Ch. 3
11.1 IV Topology with filters Notes
12.1 IV Tychonoff's theorem Munkres, §37
12.2 IV Examples
13.1 cancelled
13.2 V Function spaces Munkres, §46
14 no lectures in Week 14
15.1 no lecture on Apr 7
15.2 Recap
16.1 V Local compactness Munkres, §29
16.2 V Adjoint constructions Munkres, §46
17.1 Exercises, problems, questions, …
17.2 Exercises, problems, questions, …
18.1 Exercises, problems, questions, …
18.2 no lecture on May 1


Exercises will be done in class during the lecture time.
In addition, the file exercises.pdf, which will be updated regularly during the semester, also contains a list of exercises.

Exam Info

  • There will be a written examination on May 22, 2015.
  • No printed or hand-written support material is allowed. A specific basic calculator is allowed.
  • See here for more information.
  • Old exams, as a 2.3 MB zip archive: old

Reference Group

  • Marianne Stornes (BMAT)
  • Marit Buset Langfeldt (MSMNFMA)
  • Xenia Voellmy (IMEDIV/MN)
2016-06-06, Markus Szymik