Course - General Topology - MA3002
General Topology
About
About the course
Course content
The content may vary, but the course normally contains the following topics: topological spaces, metric spaces, continuous functions, product topologies, separation, quotient topologies, nets and filters, countability, compactness, metrizable spaces, connectedness. The course will be lectured every second year, next time spring 2011.
Learning outcome
In the course General Topology one studies general closeness- and distance concepts. Abstract open and closed sets are being introduced, and used to define and study the general concept of continuity. Connectedness is also introduced, and closed and bounded subsets are generalized to compact spaces. Topological spaces encompass metric spaces. In many applications it has turned out to be very useful to apply these abstract consepts. The course offers good training in mathematical reasoning, and is recommended for all graduate students independent of their special field of interest.
Learning methods and activities
Lectures.
Recommended previous knowledge
TMA4100 Calculus 1, TMA4105 Calculus 2, TMA4115 Calculus 3 and TMA4120 Calculus 4K or MA1101 Basic Calculus I, MA1102 Basic Calculus II, MA1103 Vector Calculus, MA1201 Linear Algebra and Geometry, MA1202 Linear Algebra with Applications and MA2104 Differential Equations and Complex Function Theory.
Course materials
Will be announced at the start of the course.
Subject areas
- Mathematics