Introduction to Topology
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
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.
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
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.
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2
Courses and Schedule
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.
K. Jänich, Topologie, Springer.
J. R. Munkres, Topology, Prentice Hall.
B. v. Querenburg, Mengentheoretische Topologie, Springer.
G. Laures, M. Szymik, Grundkurs Topologie, Springer.
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.
The exam may be repeated at the end of the semester.