Norsk
Course MAT242

# Topology

## Course offered:

### Course offered by

 Number of credits 10 Course offered (semester) Autumn Schedule Schedule Reading list Reading list

English

None

### 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.

Autumn

English

### Aim 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.

None

### Recommended previous knowledge

MAT121 Linear Algebra and MAT211 Real Analysis

Oral examination