Topology

Education facts

Code: MMA100

In this course you will study the basic concepts of set topology, which is used in almost all modern mathematics. From analysis in several variables you will be familiar with the space R^n and its concept of distance. Instead of using the concept of distance between points, topology begins by designating a collection of subsets of a fixed set as open sets. From this, we will build up the theory of topological spaces and continuous functions. Classical continuity arguments can now be used in new situations. An interesting question to ask is whether two spaces are equivalent (homeomorphic). Sometimes we can see that the answer is "no" by using compactness or connectedness; a compact space cannot be homeomorphic with a non-compact one, nor a connected space with a non-connected one. These topological invariants are quite coarse. A finer invariant is the fundamental group of a topological space, which also connects the subject with algebra.

Entry requirements

Knowledge equivalent to 90 credits in mathematics, including the course MMG500 Algebraic Structures.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Topology

  University of Gothenburg

  Start date: 20 January 2025

  End date: 23 March 2025

  Pace of study: 50 %