TSI群作用的缺集

摘要：

在一个温和的可定义性假设下，我们刻画了波兰空间上的tsi波兰群的Borel作用族$Γ\curvearrowright X$，该作用族可分解为可数个允许完备Borel集的作用，这些完备Borel集相对于$1_Γ$的开邻域是缺集的。在$Γ$是非阿基米德的特殊情况下，当且仅当$\mathbb{E}_0^{\mathbb{N}}$没有连续嵌入到$E_Γ^X$中时，才有这样的分解。

英文摘要：

Under a mild definability assumption, we characterize the family of Borel actions $Γ\curvearrowright X$ of tsi Polish groups on Polish spaces that can be decomposed into countably-many actions admitting complete Borel sets that are lacunary with respect to an open neighborhood of $1_Γ$. In the special case that $Γ$ is non-archimedean, it follows that there is such a decomposition if and only if there is no continuous embedding of $\mathbb{E}_0^{\mathbb{N}}$ into $E_Γ^X$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。