论文标题
轨道假测量和Gromov-Hausdorff距离的普遍性
Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance
论文作者
论文摘要
我们考虑了Cúth，doucha和kurka最近引入和研究的标准鲍尔空间上的伪测量学之间的borel降低性概念，以及轨道伪计的概念，这是轨道等价关系概念的连续版本。众所周知，波兰度量空间等轴测的关系与通用轨道对等关系相比是可见的。我们证明了假数测量法的一个版本，这表明波兰度量空间的Gromov-Hausdorff距离是可以在特定类别的轨道假数中的通用元素来获得的。
We consider the notion of Borel reducibility between pseudometrics on standard Borel spaces introduced and studied recently by Cúth, Doucha and Kurka, as well as the notion of an orbit pseudometric, a continuous version of the notion of an orbit equivalence relation. It is well known that the relation of isometry of Polish metric spaces is bireducible with a universal orbit equivalence relation. We prove a version of this result for pseudometrics, showing that the Gromov-Hausdorff distance of Polish metric spaces is bireducible with a universal element in a certain class of orbit pseudometrics.
