| dc.contributor.advisor | Chodounský, David | |
| dc.creator | Grebík, Jan | |
| dc.date.accessioned | 2021-01-15T16:31:11Z | |
| dc.date.available | 2021-01-15T16:31:11Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/123575 | |
| dc.description.abstract | Práce se zabýva otázkami teorie grafu v kontextu deskriptivní teorie množin. Hlavní objekty studia jsou graphony, graphingy a variace na graf G0. Představíme přistup ke kompaktnosti prostoru graphonu pomocí slabě* topologie a pojem frakcionalního isomor- fismu graphonu. Použijeme variantu G0-dichotomie v kontextu klasifikačního problému. Dokážeme měritelnou verzi Vizingovi věty pro grafingy. 1 | cs_CZ |
| dc.description.abstract | In this thesis we consider various questions and problems about graphs that appear in the framework of descriptive set theory. The main object of study are graphons, graphings and variations of the graph G0. We establish an approach to the compactness of the graphon space via the weak* topology and introduce the notion of a fractional isomorphism for graphons. We use a variant of the G0-dichotomy in the context of the classification problem. Finally, we show a measurable version of the Vizing's theorem for graphings. 1 | en_US |
| dc.language | English | cs_CZ |
| dc.language.iso | en_US | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.subject | graphs | en_US |
| dc.subject | graphons | en_US |
| dc.subject | graphings | en_US |
| dc.subject | dichotomy | en_US |
| dc.subject | Borel reducibility | en_US |
| dc.subject | orbit equivalence relation | en_US |
| dc.subject | Polish group | en_US |
| dc.subject | grafy | cs_CZ |
| dc.subject | graphony | cs_CZ |
| dc.subject | graphingy | cs_CZ |
| dc.subject | dichotomie | cs_CZ |
| dc.subject | Borelovska reducibilita | cs_CZ |
| dc.subject | orbitova equivalence | cs_CZ |
| dc.subject | Polska grupa | cs_CZ |
| dc.title | Definable graphs | en_US |
| dc.type | dizertační práce | cs_CZ |
| dcterms.created | 2020 | |
| dcterms.dateAccepted | 2020-05-05 | |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.identifier.repId | 177569 | |
| dc.title.translated | Definovatelne grafy | cs_CZ |
| dc.contributor.referee | Kurka, Ondřej | |
| dc.contributor.referee | Zapletal, Jindřich | |
| dc.identifier.aleph | 002391289 | |
| thesis.degree.name | Ph.D. | |
| thesis.degree.level | doktorské | cs_CZ |
| thesis.degree.discipline | Algebra, number theory, and mathematical logic | en_US |
| thesis.degree.discipline | Algebra, teorie čísel a matematická logika | cs_CZ |
| thesis.degree.program | Algebra, number theory, and mathematical logic | en_US |
| thesis.degree.program | Algebra, teorie čísel a matematická logika | cs_CZ |
| uk.thesis.type | dizertační práce | cs_CZ |
| uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
| uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
| uk.faculty-abbr.cs | MFF | cs_CZ |
| uk.degree-discipline.cs | Algebra, teorie čísel a matematická logika | cs_CZ |
| uk.degree-discipline.en | Algebra, number theory, and mathematical logic | en_US |
| uk.degree-program.cs | Algebra, teorie čísel a matematická logika | cs_CZ |
| uk.degree-program.en | Algebra, number theory, and mathematical logic | en_US |
| thesis.grade.cs | Prospěl/a | cs_CZ |
| thesis.grade.en | Pass | en_US |
| uk.abstract.cs | Práce se zabýva otázkami teorie grafu v kontextu deskriptivní teorie množin. Hlavní objekty studia jsou graphony, graphingy a variace na graf G0. Představíme přistup ke kompaktnosti prostoru graphonu pomocí slabě* topologie a pojem frakcionalního isomor- fismu graphonu. Použijeme variantu G0-dichotomie v kontextu klasifikačního problému. Dokážeme měritelnou verzi Vizingovi věty pro grafingy. 1 | cs_CZ |
| uk.abstract.en | In this thesis we consider various questions and problems about graphs that appear in the framework of descriptive set theory. The main object of study are graphons, graphings and variations of the graph G0. We establish an approach to the compactness of the graphon space via the weak* topology and introduce the notion of a fractional isomorphism for graphons. We use a variant of the G0-dichotomy in the context of the classification problem. Finally, we show a measurable version of the Vizing's theorem for graphings. 1 | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| thesis.grade.code | P | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | O | |
| uk.departmentExternal.name | Matematický ústav AV ČR, v.v.i. | cs |
| dc.identifier.lisID | 990023912890106986 | |
