Isometric Embeddings of Bounded Metric Spaces into the Gromov-Hausdorff Class

Abstract

It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic metric space. This description is interesting in itself. The technique of optimal correspondences and their distortions is used.

15 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2111.06709