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Metric spaces

Code: 92995
ECTS: 5.0
Lecturers in charge: doc. dr. sc. Maja Resman - Lectures
prof. dr. sc. Sonja Štimac - 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 students to the structures of metric and topological spaces.

COURSE DESCRIPTION AND SYLLABUS (by weeks):
1. Basic and more complex examples from mathematical analysis and motivation for the concept of metric space;
2. Metric spaces. Examples, open and closed sets, equivalent metrics, continuous mappings;
3. Topological spaces. Topological structures, basis, subbasis, subspaces, product of spaces, quotion space, homeomorphism;
4. Hausdorff's spaces. Examples, properties, continuous mapping on compact space, compactness in Rn , uniform continuous mappings and compactness;
5. Connected spaces.
6. Complete metric spaces. Banach's theorem, Cantor's theorem, Baire's theorem, completeness of metric space;
7. Arzela-Ascolli's theorem.
Literature:
  1. S. Mardešić: Matematička analiza u n-dimenzionalnom realnom prostoru I
  2. W. Sutherland: Introduction to Metric and Topological Spaces
  3. J. Dugundji: Topology
  4. Z. Čerin: Metrički prostori
  5. K. Jänich: Topology
1. semester
Analiza - Regular study - Mathematics Education

2. semester
Analiza - Regular study - Mathematics Education
Consultations schedule: