Subjects

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

Metric and Normed Spaces - OKBM3M046A

Title:	Metrické a normované prostory
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2023
Semester:	summer
E-Credits:	4
Examination process:	summer s.:
Hours per week, examination:	summer s.:0/0, Ex [HT]
Extent per academic year:	10 [hours]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	combined
Note:	course can be enrolled in outside the study plan enabled for web enrollment priority enrollment if the course is part of the study plan

Guarantor:	RNDr. František Mošna, Ph.D.
Teacher(s):	prof. RNDr. Jarmila Novotná, CSc.
Pre-requisite :	OKBM3M023A

Opinion survey results Examination dates Noticeboard

Annotation -

In the course, basic concepts from the theory of metric and normed spaces. Concepts as neighbourhood, convergence, metric, norm, complete metric space, compact space are dealt with. The course offers a deeper and more general perspective on some parts of algebra and calculus. Understanding the topic on the base of examples is emphasized.

Last update: Novotná Jarmila, prof. RNDr., CSc. (23.01.2024)

Descriptors - Czech

Celkem kreditů: 4 .... 120 h

Přímá výuka:

- prezenční forma studia: 10 h

- kombinovaná forma studia. 10 h

Příprava na výuku, plnění domácích úkolů:

- prezenční forma studia: 45 h

- kombinovaná forma studia: 45 h

Příprava na zkoušku:

- prezenční forma studia: 65 h

- kombinovaná forma studia 65 h

Last update: Novotná Jarmila, prof. RNDr., CSc. (23.01.2024)

Course completion requirements -

The course is taught only in Czech, so the requirements are only in Czech

Last update: Novotná Jarmila, prof. RNDr., CSc. (23.01.2024)

Literature - Czech

DOŠLÁ, Z., DOŠLÝ, O. Metrické prostory, Teorie a příklady, MU Brno 2006. (https://is.muni.cz/th/143424/fi_b/cd-priloha/skripta/mp/metricke-prostory-pro-obrazovku.pdf?so=nx)

KOSMÁK, L., POTŮČEK, R Metrické prostory, Academia, Praha 2004.

NETUKA, I. Základy moderní analýzy, Matfyzpress Praha 2014.

KOSTYRKO, P., ŠALÁT, T. Metrické prostory. Praha, SPN, 1976.

https://www2.karlin.mff.cuni.cz/~jvesely/ma13-14/MFF/MMA/kapi12.pdf

Základní přehled lze získat např. na:

https://cs.wikipedia.org/wiki/Metrick%C3%BD_prostor

https://cs.wikipedia.org/wiki/Normovan%C3%BD_line%C3%A1rn%C3%AD_prostor

https://cs.wikipedia.org/wiki/Topologick%C3%BD_prostor

https://cs.wikipedia.org/wiki/Konvergence

https://cs.wikipedia.org/wiki/Kompaktn%C3%AD_mno%C5%BEina

Last update: Novotná Jarmila, prof. RNDr., CSc. (03.01.2023)

Syllabus -

• Scalar product, Inner product space, orthogonality

• Metric, metric space

• Norm, ed space

• Open and closed sets, interior, boundary and closure of a set

• Convergency, completeness

• Continuous mappings

• Examples of spaces of sequences and functions

Last update: Novotná Jarmila, prof. RNDr., CSc. (23.01.2024)

Learning resources - Czech

https://dl1.cuni.cz/course/view.php?id=7624

Last update: Novotná Jarmila, prof. RNDr., CSc. (23.01.2024)