Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

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

Opinion survey results Examination dates SS schedule Noticeboard

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.

Course completion requirements -

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

Following the lessons.

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.

Teaching methods -

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

The goals are examples and applications.

Requirements to the exam -

Last update: doc. RNDr. Pavel Pyrih, CSc. (30.04.2020)

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.

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.