Postgraduate course

Course description

Objectives and Content

One studies topological spaces. An important part is to attach algebraic and combinatorial invariants to these spaces.

Learning Outcomes

After successful completion of the course the student will be able to:

  • Give basic properties and results related to topological spaces and algebraic topology.
  • Describe and give examples of the product topology, subspace topology, metric topology and the quotient topology and be able to deduce the basic properties of these topologies.
  • Explain the main ideas in the proof of Urysohns metrization theorem, including Urysohns lemma, and the the Borsuk-Ulam theorem.
  • Explain the main ideas leading to the development of the fundamental group of the circle and the n-sphere.

Semester of Instruction

Required Previous Knowledge
Recommended Previous Knowledge
MAT121 Linear Algebra and MAT211 Real Analysis
Credit Reduction due to Course Overlap
M233: 10 ECTS
Forms of Assessment
Oral examination
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.