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Topology and functional analisis

General data

Course ID: WM-MA-S2-E2-AFIT
Erasmus code / ISCED: (unknown) / (unknown)
Course title: Topology and functional analisis
Name in Polish: Analiza funkcjonalna i topologia
Organizational unit: Faculty of Mathematics and Natural Sciences. School of Exact Sciences.
Course groups:
ECTS credit allocation (and other scores): 0 OR 5.00 (depends on study program) Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.
view allocation of credits
Language: Polish
Subject level:

elementary
Learning outcome code/codes:

enter learning outcome code/codes
Short description:

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.
Full description:

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.
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.

Classes in period "Summer semester 2021/22" (past)

Time span: 2022-02-01 - 2022-06-30
Selected timetable range:
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Type of class:
Classes, 30 hours more information
Lectures, 30 hours more information
Coordinators: Bogdan Węglorz
Group instructors: Bogdan Węglorz
Students list: (inaccessible to you)
Examination: examination
(in Polish) E-Learning:

(in Polish) E-Learning (pełny kurs) z podziałem na grupy
Type of subject:

obligatory
(in Polish) Grupa przedmiotów ogólnouczenianych:

(in Polish) nie dotyczy
Course descriptions are protected by copyright.
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