A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group
A Metamathematical Condition Equivalent to the Existence of a Complete Left Invariant Metric for a Polish Group
复制标题
等价于波兰群完全左不变度量存在性的元数学条件
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Alex Thompson
中科院分区：
文献类型：
--
作者：
Alex Thompson
本文加强了Hjorth的一个定理，给出了Polish群容许相容完备左不变度量的一个新的刻划。作为推论，证明了任何不具有完备左不变度量的波兰群在其轨道等价关系本质上不可数的波兰空间上具有连续作用。
Abstract Strengthening a theorem of Hjorth this paper gives a new characterization of which Polish groups admit compatible complete left invariant metrics. As a corollary it is proved that any Polish group without a complete left invariant metric has a continuous action on a Polish space whose associated orbit equivalence relation is not essentially countable.