MA3002 General Topology - Spring 2016


  • I have uploaded the file exam2016.pdf that has the exam problems with hints for solutions.
  • There will be no lecture on Tuesday, March 8th.
  • The first meeting will be on Tuesday, January 12th.
  • Actually this and the one above have good chances to be the only messages that will appear here during the course, because of I will try to use itslearning for a lot of communication in this course.


  • I have already established two forums, one for questions concerning the formal aspects of this course, and one for the purpose of discussing the mathematics. Please make ample use of them.
  • And now there are also two links: One to this page, and on to the lecture notes. :-) Warning: :-| Don't get excited! :-( As of now, it's not much more than a copy of the table below. m( The actual contents will be filled in as the course proceeds…

Course Information


  • Tuesdays, 10:15 - 12:00, KJL24 R54
  • Thursdays, 12:15 - 14:00, KJL21 G21


  • Office: 1252, Sentralbygg II
  • Hours: On Tuesdays after the lecture. Whenever you have a question, don't hesitate to come by my office and ask me.


I intend that

  • notes for the course

are produced. Details will be supplied in the lectures.

Here is a (freely available) set of notes that points out a lot of applications of topology to real world problems.

Therefore we will not have to work with a text book. There is, however, an 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. 2. Aufl. Springer Spektrum, Heidelberg, 2015. (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.

Table of Contents

The syllabus is defined in terms of the official course text.

  • 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

Part I: Continuous maps

  • 2.1 Happy New Year and Welcome to (General) Topology!
    Course text reference: Munkres, §20
    How to prepare: Ø
  • 2.2 Metric spaces
    Course text reference: Munkres, §21
  • 3.1 Topological spaces
    Course text reference: Munkres, §12
  • 3.2 Continuous maps
    Course text reference: Munkres, §18
  • 4.1 Closed subsets
    Course text reference: Munkres, §17
  • 4.2 Bases
    Course text reference: Munkres, §13

Part II: Universal properties

  • 5.1 Subspaces
    Course text reference: Munkres, §16
  • 5.2 Quotients
    Course text reference: Munkres, §22
  • 6.1 Products
    Course text reference: Munkres, §15
  • 6.2 Sums

Part III: Topological properties

  • 7.1 Connectivity
    Course text reference: Munkres, §23
  • 7.2 Path connectivity
    Course text reference: Munkres, §24
  • 8.1 Hausdorff spaces
    Course text reference: Munkres, §31
  • 8.2 Separated maps
  • 9.1 Compact spaces
    Course text reference: Munkres, §26
  • 9.2 Proper maps
    Course text reference: Munkres, §27
  • 10.1 Compact subspaces of the real line
    Course text reference: Munkres, §19

Part IV: Nets and filters

  • 10.2 Nets, filters, and convergence
    Course text reference: Munkres, Supp. Ch. 3
  • 11.1 Topology with filters
  • 11.1 Tychonoff's theorem
  • 12.1 Winter/Spring break
  • 12.2 Winter/Spring break
  • 13.1 Winter/Spring break
  • 13.2 Examples

Part V: Function spaces

  • 14.1 Function spaces
    Course text reference: Munkres, §46
  • 14.2 Local compactness
    Course text reference: Munkres, §29
  • 15.1 Adjoint constructions
    Course text reference: Munkres, §46
  • 15.2
  • 16.1
  • 16.2
  • 17.1


Exercises will be done in class during the lecture time.

Exam Info

  • The exam is on 2016-06-06 at 09:00.
  • See here for the offical information.
  • The file exam2015.pdf has the exam problems from last year with hints for solutions.
  • The 2.3MB zip archive old contains some older exams.

Reference Group

  • Didrik Fosse
  • Maria Alonso Jacome
2016-06-16, Markus Szymik