244 research outputs found
A hierarchy on non-archimedean Polish groups admitting a compatible complete left-invariant metric
In this article, we introduce a hierarchy on the class of non-archimedean
Polish groups that admit a compatible complete left-invariant metric. We denote
this hierarchy by -CLI and L--CLI where is a countable
ordinal. We establish three results:
\begin{enumerate}
\item is -CLI iff ;
\item is -CLI iff admits a compatible complete two-sided invariant
metric; and
\item is L--CLI iff is locally -CLI, i.e.,
contains an open subgroup that is -CLI.
\end{enumerate}
Subsequently, we show this hierarchy is proper by constructing
non-archimedean CLI Polish groups and for
, such that
\begin{enumerate}
\item is -CLI but not L--CLI for ;
and
\item is -CLI but not L--CLI.
\end{enumerate}Comment: 20 pages, submitte
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