Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes

Autor: Ivanov, A. O., Lychagina, E. S., Tuzhilin, A. A.
Rok vydání: 2024
Předmět:
Druh dokumentu: Working Paper
Popis: In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance) is investigated. It is easy to construct an example of non-isometric metric spaces such that the Gromov--Hausdorff distance between them vanishes. Such spaces are non-distinguishable, of course. But we give examples of non-distinguishable metric spaces, the Gromov--Hausdorff distance between which is non-zero. More over, we prove several sufficient and necessary conditions for metric spaces to be non-distinguishable.
Comment: 14 pages, 2 figures
Databáze: arXiv