SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Metric Spaces - NMMA164
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: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Mgr. Benjamin Vejnar, Ph.D.
doc. 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 -
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 -

The exam is oral and its range depends on the lecture.

Last update: Cúth Marek, doc. Mgr., Ph.D. (01.02.2022)
Literature -

Literature will be specified during the first lecture.

Last update: Vejnar Benjamin, doc. Mgr., Ph.D. (29.10.2019)
Teaching methods - Czech

Studenti si dělají zápisky z přednášek, kde lektor vykládá látku

Last update: Cúth Marek, doc. Mgr., Ph.D. (01.02.2022)
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)
 
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