Topology and functional analisis WM-MA-S2-E2-AFIT
1. Topology and topological spaces. Metric spaces.
2. From metric spaces to topology. Accumulation points and limits.
3. Subspaces and continuous functions.
4. Another constructions of topological spacs.
5. Borel sets and Baire sets.
6. Other separation axioms.
7. Almost topological properties (completeness).
8. Compact spaces. Completeness and compactness.
9. Convex and very unconvect spaces.
10. Banach spaces.
11. Continuous functions. Weierstrass theorem, Stone's theorem, Urysohn's lemma and Tietze-Urysohn theorem.
12. Hilbert theorem, ortogonality. Classical Fouriera series.
13. Continuous linear functionals. Weak and *-weak convergence.
14. Applications of Baire theorem.
15. Linear topologies. Weak topologies in Banacha spaces.
(in Polish) E-Learning
(in Polish) Grupa przedmiotów ogólnouczenianych
Subject level
Learning outcome code/codes
Type of subject
Course coordinators
Bibliography
- Bogdan Węglorz, TOPOLOGIA, Wydawnictwo Naukowe UKSW, Warszawa 2017,
- Tadeusz Pytlik, ANALIZA FUNKCJONALNA, Instytut Matematyczny Uniwersytetu Wrocławskiego, Wrocław 2000.
Additional (more general) hanbooks:
- R. Engelking, TOPOLOGIA OGÓLNA, PWN Warszawa 1989;
- W. Rudin, ANALIZA FUNKCJONALNA, PWN Warszawa 2001.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: