Czech

Not applicable.

All knowledge of the courses oriented on algebra and analysis that are taught in the bachelor's and master's study of Mathematical Engineering.

Students are to pass an exam consisting of the written and oral parts. During the exam, their knowledge of the concepts introduced and of the basic propertief of these concepts will be assessed. Also their ability to use theoretic results for solving concrete problems will be evaluated.
The attendance of lectures is not compulsory and, therefore, it will not be checked.

The aim of the course is to make the students acquitant with basics of topology and with topological methods frequently used in other mathematical disciplines and in computer science.
The students will acquire knowledge of basic topological concepts and their properties and will understand the important role topology playes in mathematical analysis. They will also learn to solve simple topological problems and apply the results obtained into other mathematical disciplines and computer science

Not applicable.

Not applicable.

E. Čech, Topological spaces, in: Topological Papers of Eduard Čech, ch. 28, Academia, Prague, 1968, 436 - 472. (EN)
N. Bourbali, Elements of Mathematics - General Topology, Chap. 1-4, Springer-Verlag, Berlin, 1989. (EN)
J.L.Kelly, General Topology, Springer-Verlag, 1975. (EN)
N.M.Martin and S. Pollard,Closure Spacers and Logic, Kluwer Acad. Publ., Dordrecht, 1996. (EN)
S. Vickers, Topology Via Logic, Cambridge University Press, New York, 1989. (EN)
R.W. Hall, G.T. Hermann, Y. Kong and R. Kopperman, Digital Topology (Theory and Applications), Springer, 2006 (EN)

J. Adámek, V. Koubek a J. Reiterman, Základy obecné topologie, SNTL, Praha, 1977. (CS)
E. Čech, Topologické prostory, Nakladatelství ČSAV, Praha, 1959. (CS)
T. Y. Kong and A. Rosenfeld, Digital topology: introduction and survey, Computer Vision, Graphics, and Image Processing 48(3), 1989, 357 - 393. Publisher Academic Press Professional, Inc. San Diego, CA, USA (EN)
E. Čech, Topological spaces (Revised by Z. Frolík mand M. Katětov), Academia, Prague, 1966. (EN)
R. Engelking, General Topology,Panstwowe Wydawnictwo Naukowe, Warszawa, 1977. (EN)

20 hours, optionally

1. Basic concepts of set theory
2. Axiomatic system of closure operators
3. Čech closure operators
4. Continuous mappings
5. Kuratowski closure operators and topologies
6. Basic properties of topological spaces
7. Compactness and connectedness
8. Metric spaces
9. Closure operators in algebra and logic
10. Introduction to digital topology