1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
Introduce the students to some basic topological facts and methods as a followup of ideas they encounterd earlier in analysis, geometry and elewhere.

COURSE DESCRIPTION AND SYLLABUS:
Subjects by weeks:
1. From metric to topological spaces. Separation axioms.
2. Normal spaces. Urysohn's lemma. Tietze's extension theorem.
3. Connectedness. Path connectedness. Local (path) connectedness.
4. Compactness. Sigma-compactness. Local compacness.
5. Baire spaces. Compactification.
6. Product of topological spaces. Tyhonov's theorem.
7. Inverse systems and inverse limits. Dyadic solenoid.
8. Function spaces. Topology of pointwise convergence, topology of uniform convergence and comptact-open topology.
9. Quotient and adjunction spaces. Orbit spaces.
10. Weak and strong topology. CW complexes.
11. Paracompactness. Partition of unity.
12. Metrizability of topological spaces.
13. Extending continuous maps. Homotopy.

Enrollment :
Attended : Metric spaces

Examination :
Passed : Metric spaces

Mandatory course - Regular study - Theoretical Mathematics