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From the topological point of view a continuum is a compact connected metric space. The course will be devoted
to the study of further topological properties of a continuum. An important part will be the constructions of various
continua, which are the basic stones in a other math fields.
Last update: T_KMA (16.05.2012)
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Following the lessons. Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
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Sam B. Nadler, Jr, Continuum theory. An introduction. Pure and Applied Mathematics, Marcel Dekker (1992) ISBN 0-8247-8659-9. Last update: T_KMA (16.05.2012)
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The goals are examples and applications. Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
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The exam has an oral form with written preparation. The student will be given a topic for which he will prepare related sentences, definitions and evidence.
The form of the exam will be full-time or distance and will always be specified in the SIS for individual dates.
The full-time form of the exam will take place in the lecture room listed in the SIS.
The distance form of the exam will take place in the Zoom environment and will be a modification of the full-time form. Last update: Pyrih Pavel, doc. RNDr., CSc. (30.04.2020)
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The course will cover all basic topics from Continuum theory:
1. The construction of continua as nested sequences
2. Continuum as a inverse limit
3. Decomposition of continua
4. Theorems about limits
5. Boundary bumping theorem
6. Existence of non-cut points
7. A general mapping theorem
8. Peano continua
9. Graphs
10. Dendrites
11. Irreducible continua
12. Arc-like continua
13.Special types of maps and their properties Last update: T_KMA (16.05.2012)
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For the course one year of study at any specialization on MFF is sufficient. Last update: Pyrih Pavel, doc. RNDr., CSc. (07.05.2018)
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