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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00617746" target="_blank" >RIV/67985840:_____/25:00617746 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.topol.2024.109095" target="_blank" >https://doi.org/10.1016/j.topol.2024.109095</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2024.109095" target="_blank" >10.1016/j.topol.2024.109095</a>

Result language
angličtina
Original language name
Orbit pseudometrics and a universality property of the Gromov-Hausdorff distance
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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