VL: Topology, WS 13/14

Michael Joswig, Institut für Mathematik, TU Berlin.

Assistent: Benjamin Assarf

Contents

The course will roughly follow Armstrong's book. Most of the first eight chapters will be covered:

• Introduction
• Continuity
• Compactness and connectedness
• Identification spaces
• The fundamental group
• Triangulations
• Surfaces
• Simplicial homology

Literature on Topology

1. M.A. Armstrong: Basic topology, Springer, 1983.
2. A. Hatcher: Algebraic topology, Cambridge, 2002.
3. E. Ossa: Topologie, Mathematik, Vieweg, 2. Auflage, 2009.
4. J. Dugundji: Topology, Allyn and Bacon, 1966
5. A. Hatcher, The Kirby torus trick for surfaces, 2013, preprint: arXiv:1312.3518 (new) (concerning that every closed surface has a triangulation)

Arbitrary product topological spaces

One might look at an arbitrary product of topological spaces (finite, infinite, or even not countable). The product topology has the same definition as in the finite case. The theorem of Tychonoff says that the product of topological spaces is compact if and only if each of the factors are compact. For more information and the proof see Chapt. XI Theorem 1.4 of [4]

Final Exam

There will be a written exam during the last lecture. Meaning on the 13th of Feburary at 8:00. ATTENTION: if you achieved the requirement for the exam (50% of the homework) you are able to sign up for the final exam in QISPO (though the tubit portal). This is mandatory for the exam. If you are not a student of TU-Berlin please write an e-mail to Benjamin Assarf

Results of 1st and 2nd Exam

The results of the 1st and 2nd Exam are already send over to the "Pruefungsamt". The inspection of the exams is already over.

Exercise Sheets

• Sheet 01
• Sheet 02
• Sheet 03
• Sheet 04
• Sheet 05 (Version 2: Tue Nov 19 2013)
• Sheet 06
• Sheet 07
• Sheet 08
• Sheet 09
• Sheet 10
• Sheet 11
• Sheet 12
• Sheet 13 (last homework sheet)
• Sheet 14