Topology

Topology (MA3241)

Prof. Dr. Eva Viehmann

Stephan Neupert

Time and venue

Lecture	Mo 10:15 - 11:00 in 00.07.014 Do 10:15 - 11:45 in 00.09.022
Tutor group	Mo 11:00-11:45 in 00.07.014

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.

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