If necessary, the lessons can be given in English.
Knowledge and understanding
Know concepts and fundamental results of general topology and topological algebra, and some modern problems by noting the intrinsic difficulties.
Use a modern formal language in the formulation of topological problems.
Applied knowledge and understanding
Face and solve with an appropriate language some classical problems in topology.
Identify relations between topological questions and problems or theory from other areas of mathematics.
Solve topological problems, also beyond those treated in the course.
Cross-sectoral skills/soft skills
Autonomy of judgment
Identify techniques from algebra, set-theory, analysis or geometry, suitable to solve the assigned problems.
Evaluate the difficulties of specific problems in topology.
Communicate the arguments in general topology or topological algebra learned in the course.
Communicate to a non-specialized audience the main aspects to the classical theory of topological groups and some modern problem.
Be able to read a research article in topology concerning the arguments of the course.
Autonomously work in the bibliographical search.
Face the proposed problem, selecting the more meaningful ones.
Introduction to Topological Groups and the Pontryagin-van Kampen Duality.