Metric Spaces - NMMA164
Title: Metrické prostory Department of Mathematical Analysis (32-KMA) Faculty of Mathematics and Physics from 2018 summer 3 summer s.:2/0, Ex [HT] unlimited unlimited no no taught Czech full-time full-time
Guarantor: doc. Mgr. Benjamin Vejnar, Ph.D.doc. Mgr. Marek Cúth, Ph.D.RNDr. Martin Rmoutil, Ph.D. doc. Mgr. Marek Cúth, Ph.D.RNDr. Martin Rmoutil, Ph.D.doc. Mgr. Benjamin Vejnar, Ph.D. M Bc. OMM Bc. OM > Doporučené volitelné Mathematics > Real and Complex Analysis, Topology and Category NMAA006
 Annotation - ---CzechEnglish
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 - ---CzechEnglish

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

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

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 - ---CzechEnglish

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)