PřF:M6140 Topology - Course Information
M6140 Topology
Faculty of ScienceSpring 2005
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jiří Rosický, DrSc. (lecturer)
- Guaranteed by
- prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc. - Timetable
- Mon 12:00–13:50 N21
- Timetable of Seminar Groups:
- Prerequisites
- M3100 Mathematical Analysis III
Mathematical analysis: continuous functions, metric spaces - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The course presents one of basic disciplines of modern mathematics. It naturally follows the well-known concepts af a metric space and a continuous function. It introduces topological spaces and presents their basic properties connected with separability, connectedness and compactness. There are considered real valued continuous functions on topological spaces as well. Finally, there is proved Brouwer's fix-point theorem and there is shown how the fundamental group provides a simple proof of the fundamental theorem of algebra.
- Syllabus
- 1. Topological spaces: definition, examples 2. Continuous maps: continuous maps, homeomorphisms 3. Subspaces and products: subspaces, products 4. Axioms of separability: Kuratowski spaces, Hausdorff spaces, regular spaces, normal spaces 5. Compact spaces: compactness, basic properties, Tychonoff's theorem 6. Connected spaces: connectedness, components, product of connected spaces, arcwise connected spaces, locally connected spaces, continua, Cantor discontinuum 7. Homotopies: definition, basic properties, simple connected spaces, fundamental group, Brouwer's theorem in dimension 2, fundamental theorem of algebra 8. Real valued functions: completely regular spaces, Urysohn's theorem, Tietze's theorem 9. Locally compact spaces: definition, basic properties, one-point compactification 10. Brouwer's theorem: complexes, triangulation, Sperner's lemma, Brouwer's theorem
- Literature
- PULTR, Aleš. Podprostory euklidovských prostorů. Vyd. 1. Praha: SNTL - Státní nakladatelství technické literatury, 1986, 253 s. info
- CHVALINA, Jan. Obecná topologie. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1984, 193 s. info
- PULTR, Aleš. Úvod do topologie a geometrie. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 231 s. info
- Assessment methods (in Czech)
- Výuka: přednáška, Zkouška: ústní
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course is taught annually.
- Enrolment Statistics (Spring 2005, recent)
- Permalink: https://is.muni.cz/course/sci/spring2005/M6140