Topology

About this programme

No fees are charged for EU and EEA citizens, Swedish residence permit holders and exchange students. 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. Knowledge equivalent to 90 credits in mathematics, including the course MMG500 Algebraic Structures. All eligible applicants who have applied before the deadline will be granted a place. Mathematical Sciences is a joint department of Chalmers/University of Gothenburg. Your education takes place in the spacious and bright premises of Mathematical Sciences at the Chalmers campus Johanneberg, where there are lecture halls, computer rooms and group rooms. Here you can also find student lunch room and reading room, as well as student counsell