##### Winter semester 2017/18

### Topology

### General Information

Lecturer

Creditpoints

6 ECTS

First lecture

Wednesday, 18/10/17, 12 pm

Appointments

On Wednesdays, 12 pm, lecture room IV

Inhalt

The lecture is an introduction into set-theoretic topology.
The topics of the lecture include: compactness, product topologies, Urysohn's Lemma and Tietze's Extension theorem,
continuous partitions of unity, metrization theorems, Stone-Weierstraß theorem.

Prerequisites

Analysis I, Analysis II

Office hours

You can come to office 416 in building E2 4 at any time
if you have questions about the organization or the content of this lecture.

### Exams

Criteria

50% of the achievable points from
the exercise sheets; Passing of an exam

Type of exam

Written exam

Examination dates

The first written exam will take place on the 5th of February in 2018 in lecture room 3 at 9 am.
The second written exam will take place on the 6th of April in 2018 in lecture room 3 at 9 pm. Both exams will be written and take 3 hours.
You will be allowed to bring a handwritten two-sided DinA4 sheet, but no further auxilliary materials are permitted. To pass this lecture, you
only need to pass one of the exams.

### Tutorials service

Exercise groups

The exercise group will take place on Thursdays, 16-18 in lecture room IV (same room as the lecture). The first exercise group will take
place on the 2nd of November in 2017.
Exceptionally, the exercise group will take place in lecture room III on the 30th of November in 2017 due to a PHD colloquiuum,.

### Exercise Sheets

Sheet 1Sheet 2Sheet 3Sheet 4Sheet 5Sheet 6Sheet 7Sheet 8Sheet 9Sheet 10Sheet 11Sheet 12### Literature and lecture notes

Lecture notes

Unfortunately, Chapter 1 only exists in German. Starting with Chapter 2, the lecture notes will be in English. In the lecture, we noticed that in the proof of Theorem 3.4 in Chapter 3, while etablishing the well-definedness of F, one Delta is chosen wrongly in the downloadable lecture notes.

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9

Lecture notes by a student

A student of this course kindly offered to give me his Latex lecture notes for this course. No guarantee for the content is given.

Lecture notes

Literature

The following books can be found in the course reserve:

- Querenburg,

- Munkres,

- Simmons,

- Kelley,

- Runde,

- Querenburg,

*Mengentheoretische Topologie*, Springer.- Munkres,

*Topology. A First Course*, Prentice Hall.- Simmons,

*Topology and Modern Analysis*, McGraw-Hill.- Kelley,

*General Topology*, van Nostrand.- Runde,

*A Taste of Topology*, Springer.