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# Introduction to Topology

## Module MA5209

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Basic Information

MA5209 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from WS 2016/7 to SS 2017.

Total workloadContact hoursCredits (ECTS)
180 h 60 h 6 CP

### Content, Learning Outcome and Preconditions

#### Content

Set topology, topological spaces, metric spaces, connectedness, neighborhood bases, countability axioms, separation axioms, convergence, continuity, compactness, Theorem of Tychonov, Theorem of Uryson, homotopy equivalence, fundamental group

#### Learning Outcome

At the end of the module, students are able to analyse topological spaces with regard to topological properties like connectedness and compactness. They are able to make competent judgements about the fundamental groups of simple topological spaces. They are able to apply the standard notions of topology in various contexts and to prove some simple results in the field presented in the course.

#### Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 2 Introduction to Topology [MA5209] Bauer, U. Fri, 10:15–11:45, MI 00.07.014
eLearning
documents
UE 2 Introduction to Topology (Exercise Session) [MA5209] Bauer, U. Thu, 12:15–13:45, MI 03.08.011
and dates in groups

#### Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercises will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. The practice sessions will focus on presentation of proofs, visualization of concepts, working out sample solutions, and devising problems reflecting the content of the lecture.

blackboard

#### Literature

K. Jänich, Topologie, Springer.
J. R. Munkres, Topology, Prentice Hall.
B. v. Querenburg, Mengentheoretische Topologie, Springer.
G. Laures, M. Szymik, Grundkurs Topologie, Springer.

### Module Exam

#### Description of exams and course work

There will be a written exam, in which the students demonstrate on examples that they can reproduce, verify, and apply the definitions and statements of the lecture without auxiliary means. Some questions will only ask for a result or for reproducing a statement, while others will require a complete line of argument or a short proof.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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