Universität Wien

250025 VO Introduction to topology (2016W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Moodle

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 05.10. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.10. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.10. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.11. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.11. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.11. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.11. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.12. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.12. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.01. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.01. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.01. 13:45 - 15:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Notions like neighbourhood, convergence, continuity, connectedness already play an important role in the courses on analysis. Set theoretic topology
examines the properties of these notions in great generality. To this end it axiomatizes the concept of neighbourhood (or equivalently that of an open set) in the central notion of topological space, i.e. a topological space is a space for which a notion of neighbourhood is available. Building on this it is possible
to define concepts like convergence, continuity, connectedness and compactness and to examine their properties. Due to the great generality of its notions topology
has applications to a wide area of mathematics and in particular then makes possible to argue using geometric intuition (based on the notion of neighbourhood). Topology thus has become a foundational theory of mathematics.

Content of the course: Departing from the courses Analysis 1 and 2 where topological notions appear for the first time we will introduce general topological spaces and study the basic topological
concepts convergence, continuity, compactness, connectedness and also techniques for constructing topological spaces.

Aims: Knowledge and understanding of basic notions and methods of topology and their properties.
Understanding of applicability of abstract notions of topology e.g. in analysis.

Assessment and permitted materials

Written exam. No aids are permitted.

Minimum requirements and assessment criteria

50 percent of the maximum score of the written exam

Examination topics

Content of the course

Reading list

v. Querenburg: Mengentheoretische Topologie

Laures, Szymik: Grundkurs Topologie

Bartsch: Allgemeine Topologie

Bourbaki: Topology

Jänich: Topologie

Schubert: Topologie

Association in the course directory

TFA

Last modified: Mo 07.09.2020 15:40