The course covers the basic notions in set topology. Set topology is a big and important keystone in modern mathematics. From calculus in several variables, you should be acquainted with the three dimensional space and its distance notions. In topology, we distance ourselves from distance notions and real valued functions. Instead, we start from a collection of subsets to a given set. The elements of the collection are called open. By using these we build a theory for topological spaces and continuous functions. Classical continuity arguments can then be used in new and often unexpected situations. Some important types of topological spaces are for example compact and coherent topological spaces. Those properties can help us to decide if two topological spaces are topologically identical, i.e. if they are homomorphic. This will e.g. induce that a compact space can not be homomorphic with a non-compact space and a coherent space can not be homomorphic with non-coherent space. This course is mainly for students who like mathematical proofs and abstractions. For those who have not taken more than one course in calculus in several variables, an insight into the world of topology can be both refreshing and eye-opening.
The information below is only for exchange students
Starts
3 November 2025
Ends
18 January 2026
Study location
Umeå
Language
English
Type of studies
Daytime,
50%
Required Knowledge
The course requires courses in Mathematics, minimum 60 ECTS or at least two years of university studies and both cases requires courses in Calculus, minimum 22,5 ECTS including a course in Multivariate Calculus minimum 7,5 ECTS, or equivalent.
Selection
Students applying for courses within a double degree exchange agreement, within the departments own agreements will be given first priority. Then will - in turn - candidates within the departments own agreements, faculty agreements, central exchange agreements and other departmental agreements be selected.
Application code
UMU-A5809
Application
This application round is only intended for nominated exchange students. Information about deadlines can be found in the e-mail instruction that nominated students receive.
Notification of admission will be sent in end of May.
