Subjects

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Metric Structures - NMAA006

Title:	Metrické struktury
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Miroslav Hušek, DrSc.
Classification:	Mathematics > Real and Complex Analysis, Topology and Category
Is incompatible with:	NMMA361, NMMA360, NMMA164

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Annotation -

Last update: T_KMA (13.05.2003)

Lipschitz maps, extension of continuous functions, Brouwer theorem, Hausdorff dimension

Syllabus -

Last update: T_KMA (13.05.2003)

1. Lipschitz and Hölder maps, their basic properties and relations, properties of function spaces of such maps (completeness, separability).

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

3. Fixed point theorems: spaces having the fixed point property, extensions of Banach theorem, Brouwer fixed point theorem and its consequences, generalization to infinite-dimensional spaces.

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