Objectives and Content
One studies topological spaces. An important part is to attach algebraic and combinatorial invariants to these spaces.
Semester of Instruction
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
Forms of Assessment
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.