2024/12/25 by A. O. Ivanov, Ivanov, A. O., E. S. Lychagina +3
Computer Science · Decision Sciences · #Digital Image Processing Techniques #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2412.18949
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.