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Load:
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1. komponenta
| Lecture type | Total |
| Lectures |
45 |
* Load is given in academic hour (1 academic hour = 45 minutes)
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Description:
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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.
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Literature:
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Matematička analiza u n-dimenzionalnom realnom prostoru I, S. Mardešić, Školska knjiga, Zagreb, 1974.
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Introduction to Metric and Topological Spaces, W. Sutherland, Oxford University Press, 1975.
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Topology, J. Dugundji, Allyn & Bacon, 1996.
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Metrički prostori, Z. Čerin, interna skripta (dostupno na web-u).
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Topology, K. Jänich, Springer Verlag, 1995.
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Pristupačnost
