This entry is from Summer semester 2018 and might be obsolete. No current equivalent could be found.

Topology (dt. Topologie)

 Level, degree of commitment Advanced 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(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Duration,frequency One semester, Regularly alternating with other advanced modules 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden.

Applicability

Module imported from B.Sc. Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Computer Science
• B.Sc. Mathematics
• M.Sc. Computer Science
• M.Sc. Mathematics
• LAaG Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.

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