The students that are approved in this curricular unit should be able to:

1. Identify and understand the fundamental concepts and results on topology;
2. Understand compactness and connectedness as topological invariants;
3. Recognize metric spaces and their properties;
4. Identify the main differences between finite-dimensional and infinite-dimensional spaces;
5. Understand the properties and the representation of linear bounded operators in Hilbert spaces;
6. Apply the Banach fixed point theorem to differential and integral equations.

Curricular Unit Form