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German original

Topology
(dt. Topologie)

Level, degree of commitment in original study programme Intermediate module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Mathematics.
Original study programme B.Sc. Mathematik / Mathematik Wahlpflichtmodule
Duration,
frequency
One semester,
Regelmäßig im Wechsel mit anderen intermediate moduleen der Geometrie
Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. Pablo Ramacher, Prof. Dr. Volkmar Welker

Contents

  • Fundamentals of set-theoretic topology: Open sets, continuous mappings.
  • Bases, construction of topological spaces, connectivity, separation properties
  • Compactness and metrizability: Central theorems on compactness,
  • metrizability conditions
  • Homotopy,: homotopy classes and equivalence, mappings of and in spheres
  • Coverings: lifting properties, fundamental group

Qualification Goals

The students

  • understand basic principles of topological structures and recognize that such structures can be found in many parts of mathematics,
  • practice the axiomatic approach and train their abstraction skills,
  • develop a deeper understanding of the implications of elementary conditions on a topological space,
  • practice mathematical methods (development of mathematical intuition and its formal justification in proofs),
  • improve their oral communication skills in the recitation class by practicing free speech in front of an audience and during discussions.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.


Recommended Reading

  • tom Dieck, Tammo: Topologie. Walter de Gruyter, 2000.
  • Jänich, K.: Topologie, Springer 2001.
  • Schubert, H.: Topologie, Teubner 1975.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.