SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Metric Spaces - NMMA164
Title in English: 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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: Mgr. Benjamin Vejnar, Ph.D.
Mgr. Marek Cúth, Ph.D.
RNDr. Martin Rmoutil, Ph.D.
Class: M Bc. OM
M Bc. OM > Doporučené volitelné
Classification: Mathematics > Real and Complex Analysis, Topology and Category
Incompatibility : NMAA006
Annotation -
Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)
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.
Course completion requirements - Czech
Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)

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

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

Literatura bude upřesněna na začátku přednášky podle vybraného tématu.

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

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.

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