We prove that the automorphism group of the Urysohn diversity is a universal Polish group. Furthermore we show that the automorphism group of the rational Urysohn diversity has ample generics, a dense conjugacy class and that it embeds densely into the automorphism group of the (full) Urysohn diversity. It follows that this latter group also has a dense conjugacy class.

中文翻译：

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普遍多样性的自同构群

我们证明了 Urysohn 多样性的自同构群是一个普遍的波兰群。此外，我们证明了有理 Urysohn 多样性的自同构群具有充足的泛型，一个密集的共轭类，并且它密集地嵌入到（完全）Urysohn 多样性的自同构群中。因此，后一组也有一个密集的共轭类。