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Metric Spaces - NMMA360

Title:	Metrické prostory
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer 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

Class:	M Bc. OM M Bc. OM > Doporučené volitelné
Classification:	Mathematics > Real and Complex Analysis, Topology and Category
Incompatibility :	NMAA006

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Non-obligatory course for the first year of study. The aim of this lecture is to provide several results about metric spaces that are deeper than in the basic course of mathematical analysis and to define some notions from topology.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)

Course completion requirements - Czech

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

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)

Literature - Czech

Literatura bude upřesněna na začátku přednášky podle vybraného tématu.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)

Syllabus -

1. Metric, metric spaces, continuous and uniformly continuous mappings, homeomorphism, isometry.

Open and closed sets, interion, closure, boundary.

Subspace, sum and product of metric spaces.

2. Totally bounded and separable metric spaces.

3. Complete metric spaces, completion, Cantor theorem, Baire theorem.

4. Compact metric spaces, Cantors discontinuum, Hilbert cube.

5. Connected metric spaces.

6. Hausdorff metric.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)