Topology

Teaching semester

Autumn

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.

Required Previous Knowledge

None

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.