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General topology

Code: 93212
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Zvonko Iljazović - Lectures
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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.
Literature:
  1. C. O. Christenson, W. L. Voxman: Aspects of Topology
  2. J. R. Munkres: Topology, 2nd edition
  3. R. Engelking: General Topology, 2nd edition
  4. J. Dugundiji: Topology
  5. J. G. Hocking, G. S. Young: Topology
  6. J. L. Kelly: General Topology
Prerequisit for:
Enrollment :
Passed : Metric spaces
1. semester
Geometrija i topologija - Regular study - Mathematics and Computer Science Education

2. semester
Geometrija i topologija - Regular study - Mathematics and Computer Science Education
Consultations schedule: