Area of Mathematics: Analysis (EA)
Semester:6ο
Course ID: 62102
Course Type:Elective
Teaching hours per week:Theory: 4Practice: 0Laboratory: 0
ECTS :5
Eclass:For the course’s material, click here.
Instructors
  • Topological Spaces: topology and topological space, basis for a topology, the subspace topology.
  • Continuous functions between topological spaces. The product topology, the metric topology.
  • Convergence: net and subnet, convergent sequences, convergent nets, continuous functions and nets.
  • Compactness: compact spaces, continuous functions and compactness, compactness in metric spaces.
  • Connectedness: connected spaces, connected components, continuous functions and connectedness.
  • Countability and Separation Axioms, the Urysohn lemma, the Urysohn metrization theorem, the Tychonoff theorem.
  • Topologies on function spaces: topology of pointwise convergence, compact-open topology.