| Area of Mathematics: | Analysis | ||
| Semester: | 1ο | ||
| Course ID: | 11102 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 1 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Stamatis Pouliasis | ||
Description
- 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.
Bibliography
- Munkres J. R., Topology, second edition, Prentice Hall, 2000.
- Kuratowski K., Topology (Volume I), Academic Press, 1966.
