On a universality property of some abelian Polish groups
On a universality property of some abelian Polish groups
复制标题
论某些阿贝尔波兰群的普遍性
DOI：
10.4064/fm179-1-1
复制
发表时间：
2002
影响因子：
0.6
通讯作者：
V. Pestov
中科院分区：
文献类型：
--
作者：
Su Gao;V. Pestov
证明了每一个交换Polish群都是强算子拓扑的可分Hilbert空间的完全酉群的闭子群的拓扑因子群。证明了由Abel Polish群作用诱导的轨道等价关系是Borel可归结为由酉群作用诱导的轨道等价关系。
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.