# MA3002 General Topology - Spring 2016

### Messages

- I have uploaded the file szymik.MA3002.pdf that has the notes for the course.

- 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.

### Itslearning

- 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. The actual contents will be filled in as the course proceeds…

### Course Information

### Lectures

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

### Lecturer

- 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.

### References

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.

- R. Ghrist. Elementary applied topology. 2014. (Appendix: Background)

www.math.upenn.edu/~ghrist/notes.html

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

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 exams.zip contains some older exams.

### Reference Group

- Didrik Fosse
- Maria Alonso Jacome