This entry is from Winter semester 2016/17 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

Students should

• understand basic principles of topological structures and recognize that such structures can be found in many parts of mathematics,
• practice axiomatic procedures and train their ability to abstract,
• develop a deeper understanding of the scope of elementary conditions on a topological space,
• practice mathematical working methods (develop mathematical intuition and its formal justification, train their ability to abstract, prove),
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion.

## Prerequisites

Translation is missing. Here is the German original:

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

## Applicability

The module 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 B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).

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.