Topology (MA3241)

 

 

Prof. Dr. Eva Viehmann

Stephan Neupert 

Time and venue

 

Content

Part 1: set topology, topological spaces, metric spaces, neighbourhood bases, countability axioms, convergence, continuity, topological products, compact spaces, separation axioms, connected spaces, Theorem of Tychonov

Part 2: fundamental group: paths, multiplication of paths, homotopy of paths, fundamental group, fundamental group of a circle, if time permits also: Brouwer Fixed Point Theorem, free groups, Theorem of Seifert and Van Kampen

Literature

G. Laures, M. Szymik: Grundkurs Topologie

 

G. Bredon: Topology and Geometry, Kapitel 1, 3

A. Hatcher: Algebraic Topology

K. Jänich: Topologie

Prerequisites

Analysis 1,2, Lineare Algebra 1,2. Interested students without these prerequisites are also welcome.

Exercises

• Exercise Sheet 1
• Exercise Sheet 2
• Exercise Sheet 3
• Exercise Sheet 4 (Correction for A11(c): Y must be (T2), not only (T1).)
• Exercise Sheet 5
• Exercise Sheet 6 (The assertion in the Lemma of Alexander is to contain a finite open subcover.)
• Exercise Sheet 7
• Exercise Sheet 8
• Exercise Sheet 9
• Exercise Sheet 10
• Exercise Sheet 11
• Exercise Sheet 12
• Exercise Sheet 13 (A36 now without a typo in the definition of t_ij)
• Exercise Sheet 14

Solutions

Here are hand-written solutions to the exercises. Please be aware, that even though prepared with some care, they may contain mistakes.

• Solutions Sheet 1
• Solutions Sheet 2
• Solutions Sheet 3
• Solutions Sheet 4
• Solutions Sheet 5
• Solutions Sheet 6
• Solutions Sheet 7
• Solutions Sheet 8
• Solutions Sheet 9
• Solutions Sheet 10
• Solutions Sheet 11
• Solutions Sheet 12
• Solutions Sheet 13

Exam

The exam will take place on February 11, 2016 from 10:00-11:30 in room MW1050.

The second exam will take place on March 31, 2016 from 12:00-13:30 in room HS 3 (00.06.011).

Office hours

Please contact us after the lecture/tutor group or write an email: "last name"@ma.tum.de