1. komponenta

Lecture type	Total
Lectures	45

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

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.

1. Matematička analiza u n-dimenzionalnom realnom prostoru I, S. Mardešić, Školska knjiga, Zagreb, 1974.
2. Introduction to Metric and Topological Spaces, W. Sutherland, Oxford University Press, 1975.
3. Topology, J. Dugundji, Allyn & Bacon, 1966.
4. Metrički prostori, Z. Čerin, interna skripta (dostupno na web-u).
5. Topology, K. Jänich, Springer Verlag, 1995.

Mandatory course - Regular study - Theoretical Mathematics