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
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:437544 |
| Date | January 2020 |
| Creators | Grebík, Jan |
| Contributors | Chodounský, David, Kurka, Ondřej, Zapletal, Jindřich |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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