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Course, academic year 2018/2019
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Topology of a continuum - NMMA363
Title in English: Topologie kontinua
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
Guarantor: doc. RNDr. Pavel Pyrih, CSc.
Mgr. Benjamin Vejnar, Ph.D.
Class: DS, geom. a topologie, gl. analýza a ob. struktury
DS, matematická analýza
DS, obecné otázky matematiky a informatiky
M Bc. OM > Zaměření MA
M Bc. OM > Zaměření MSTR
M Bc. OM > 2. ročník
Classification: Mathematics > Topology and Category
Annotation -
Last update: T_KMA (16.05.2012)
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.
Literature -
Last update: T_KMA (16.05.2012)

Sam B. Nadler, Jr, Continuum theory. An introduction. Pure and Applied Mathematics, Marcel Dekker (1992) ISBN 0-8247-8659-9.

Requirements to the exam - Czech
Last update: Mgr. Benjamin Vejnar, Ph.D. (29.09.2017)

Zkouška má ústní formu s písemnou přípravou. Studentovi bude zadáno téma, ke kterému si připraví související věty, definice a důkazy.

Syllabus -
Last update: T_KMA (16.05.2012)

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

Entry requirements -
Last update: doc. RNDr. Pavel Pyrih, CSc. (07.05.2018)

For the course one year of study at any specialization on MFF is sufficient.

 
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