Topology

What it is about

You learn the fundamentals of set-theoretic topology and algebraic topology. In the first part you analyze topological and metric spaces as well as concepts such as continuity, compactness and connectedness; in the second part you deal with homotopies, fundamental groups and singular homology. At the end of the module you can assess topological properties as well as determine fundamental groups and homology of simple spaces.

What you will be able to do

• Analyze topological spaces and metric spaces
• Form bases and neighborhood bases
• Assess countability and separation axioms
• Check compactness and connectedness
• Compute and assess fundamental groups
• Apply singular homology of simple spaces

What the module consists of

• VorlesungConveying the contents in lectures and discussions; motivation for independent study
• ÜbungDeepening through exercise sheets, solutions, initially guided, later more independent and in group work
• Studentenpräsentation / Gruppenarbeitactivating exercise format for deepening and presentation of results

Teaching method

• Online-Vorlesungen (Video)Conveying fundamentals and providing contents for pre- and post-reading
• Präsenzbesprechung (Vorlesung/Tafel/Tablet)Discussion and visualization of the contents
• Übungen mit Lösungen, Präsentationen und GruppenarbeitApplying methods and independent as well as cooperative learning