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Metric Structures - NMMA361

Title:	Metrické struktury
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2019
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

Guarantor:	prof. RNDr. Miroslav Hušek, DrSc.
Class:	M Bc. OM M Bc. OM > Doporučené volitelné
Classification:	Mathematics > Real and Complex Analysis, Topology and Category
Incompatibility :	NMAA006

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Annotation -

Last update: G_M (16.05.2012)

An elective course for bachelor's program in General Mathematics extending fundamentals of metric spaces.

Course completion requirements - Czech

Last update: prof. RNDr. Miroslav Hušek, DrSc. (13.10.2017)

Zkouška je ústní a její obsah odpovídá rozsahu, který je prezentován na přednášce.

Literature - Czech

Last update: prof. RNDr. Miroslav Hušek, DrSc. (27.10.2019)

Literatura bude upřesněna na začátku přednášky podle vybraného tématu, např.

R.Engelking: General Topology /PAN,Warszawa 1977)

K.Falconer: Fractal Geometry (John Wiley and Sons, 2003)

Syllabus -

Last update: prof. RNDr. Miroslav Hušek, DrSc. (27.10.2019)

1. Hölder maps, their basic properties and relations, properties of function spaces of such maps.

2. Eztensions of continuous, uniformly continuous and Lipschitz functions from subspaces to the whole spaces (Tietze, Katětov and other theorems).

3. Fixed point theorems: spaces having the fixed point property, extensions of Banach theorem, Brouwer fixed point theorem and its consequences, combinatorial and continuous approach.

4. Hausdorff dimension, its properties, calculation and relation to fractals.