MA3002 General Topology - Spring 2015
This is no longer a draft version of the course page. It will still be updated regularly.
- 17 Jul 2015: The re-exam will be oral.
- 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.
- 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.
- R. Ghrist. Elementary applied topology. 2014. www.math.upenn.edu/~ghrist/notes.html (Appendix: Background)
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
|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|
|4.2||I||Closed subsets||Munkres, §17|
|7.2||III||Path connectivity||Munkres, §24|
|8.1||III||Hausdorff spaces||Munkres, §31|
|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|
|13.2||V||Function spaces||Munkres, §46|
|14||no lectures in Week 14|
|15.1||no lecture on Apr 7|
|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.
- Marianne Stornes (BMAT)
- Marit Buset Langfeldt (MSMNFMA)
- Xenia Voellmy (IMEDIV/MN)