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Course, academic year 2024/2025
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Topology of a continuum - NMMA363
Title: Topologie kontinua
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
Guarantor: doc. RNDr. Pavel Pyrih, CSc.
doc. 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 -
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)
Course completion requirements -

Following the lessons.

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
Literature -

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)
Teaching methods -

The goals are examples and applications.

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
Requirements to the exam -

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)
Syllabus -

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)
Entry requirements -

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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