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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.08375 |
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| _version_ | 1866909906414600192 |
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| author | Kurka, Ondřej |
| author_facet | Kurka, Ondřej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08375 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance Kurka, Ondřej Logic Metric Geometry 54H05 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. |
| title | Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance |
| topic | Logic Metric Geometry 54H05 |
| url | https://arxiv.org/abs/2204.08375 |