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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 2013 to 2016
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter 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 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.

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.

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 two years of study at any specialization on MFF are sufficient.