English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this thesis, we study the existence of universal objets of two differentstypes in the theory of topological groups and theirs actions on compactsspaces. In the first part, we contribute to the problem of existence of testspaces for amenability. We observe that a Polish group is amenable if and onlyif its every continuous action on the Hilbert cube admits an invariantprobability measure. This generalizes a result of Bogatyi and Fedorchuk. Wealso show that actions on the Cantor space can be used to detect amenabilityand extreme amenability of Polish non-archimedean groups as well as amenabilityat infinity of discrete countable groups. As corollary, the latter property canalso be tested by actions on the Hilbert cube. These results generalise acriterion due to Giordano and de la Harpe. In the second part of this thesis weare motivated by the problem of existence of an universal topological group ofuncountable weight. We show that the group of isometries of a universalUrysohn-Katetov metric space of uncountable density is not a universal group ofthe corresponding weight. For instance, it does not contain the group ofisometries of the classical separable Urysohn metric space. This stands insharp contrast with Uspenskij's 1990 result about the group of isometries ofthe classical separable Urysohn metric space being a universal Polish group.

Actions des groupes topologiques sur les objets universels