Engelska

Varje vårtermin

The main goal of the course is to introduce students to the principles and techniques of topology, and to enable them to apply these techniques in different mathematical settings. General topology is used in other contexts as well, e.g. within data analysis and physics, in situations in which one cannot (or do not want to) define shape or closeness between points in terms of a norm (or a metric).

*topological spaces and metric spaces with examples, product topologies, continuity of functions,

*connectedness, completeness, and compactness, including the Arzela-Ascoli Theorem,

*examples of applications and topological structures,

*examples of metric and topological spaces relevant in other areas of mathematics, such as normed spaces and Hilbert spaces.

be able to give a detailed account of the fundamental topological concepts included in the course,

be able to identify the most important theorems in the course and present their proofs,

be able to explain the theory behind the methods introduced in the course,

be able to give examples of a variety of topological spaces, and explain their relevance in different areas of mathematics,

be able to recognise the topological structures in a range of mathematical problems.

be able to critically and systematically integrate knowledge from different areas of mathematics to analyse and solve complex problems using topological methods,

be able to independently and creatively identify, formulate and solve relevant problems within the framework of the course.

be able to argue for the important role of topological structures in different areas of research in mathematics and its applications,

identify the own need for further knowledge and take responsibility for further knowledge development.

Föreläsningar

Seminarier

övrigt

Homework assignments during the course.

Skriftlig tentamen

Muntlig tentamen

Completed homework
assignments can give a certain amount of bonus points that can be counted towards
the written examination; this will be specified at the start of the course.

Underkänd, godkänd

FMAF01 Mathematics - Analytic Functions and FMAF05 Mathematics - Systems and Transforms and FMAN55 Applied Mathematics.

Munkres, James R.: Topology. 2018. ISBN 9780134689517.

FMAP15F

2025-01-10

Maria Sandsten