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