Geometry and Topology MAT2304

Course content:

Matric spaces. Topology of metric spaces. Topological spaces. Basis of a topology. Continuous functions, homeomorphisms, Tietze's theorem. Connected spaces.

Compact spaces. Contiuous functions of compact spaces, Cantor's set, Cartesian products of compact spaces. Compacts subsets of n-dimensional Euclidean space.

Completeness. Baire category theorem.Banach fixed point theorem.

Homotopy theory. The fundamental group. Brouwer theorem in dimension two. Proof of the Fundamental Fundamental Theorem of Algebra

Learning outcomes: Familiarity with fundamental topological notions. Understanding of a metric and topological classification. Recognition of topological properties of subsets of an Euclidean space.