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arXiv · 2204.08375

Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance

Ondřej Kurka
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Abstract

We consider the notion of Borel reducibility between pseudometrics on standard Borel spaces introduced and studied recently by C\'{u}th, 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.

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Ondřej Kurka. 2022-04-18. Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance. https://doi.org/10.1016/j.topol.2024.109095

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