轨道伪度量与Gromov-Hausdorff距离的泛性质
Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance
AI总结：
本文研究标准Borel空间上伪度量的Borel可归约性与轨道伪度量概念，证明波兰度量空间的Gromov-Hausdorff距离与某类轨道伪度量的泛元双可归约。
摘要：
本文研究了Cúth、Doucha与Kurka近期提出并探讨的标准Borel空间上伪度量之间的Borel可归约性概念，以及作为轨道等价关系连续版本的轨道伪度量概念。众所周知，波兰度量空间的等距关系与一个泛轨道等价关系是双可归约的。本文针对伪度量证明了该结论的一个版本，表明波兰度量空间的Gromov-Hausdorff距离与某一类轨道伪度量中的一个泛元是双可归约的。
英文摘要：
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.
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。
