Alessandro Codenotti

The universal valued Abelian groups of Niemiec are L\'{e}vy, strongly exotic, extremely amenable, and $\mathbb{G}_r(0)$ is generically monothetic

We prove various properties of the universal valued Abelian groups $\mathbb{G}_r(N)$ constructed by Niemiec, for $r\in\{1,\infty\}$ and $N\in\{0,2,3,\ldots\}$. First we show that the completion of $\Gamma_0=\bigoplus_{n\in\mathbb{N}}\mathbb{Q}/\mathbb{Z}$ (for $N=0$) or $\Gamma_N=\bigoplus_{n\in\mathbb{N}}\mathbb{Z}/N\...