Geodesic
Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class
Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1400-1414

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that any bounded metric space can be embedded isometrically in the Gromov-Hausdorff metric class $\operatorname{\mathcal{G\!H}}$. This is a consequence of the description of the local geometry of $\operatorname{\mathcal{G\!H}}$ in a sufficiently small neighbourhood of a generic metric space, which is of independent interest. We use the techniques of optimal correspondences and their distortions. Bibliography: 22 titles.
Keywords: Gromov-Hausdorff distance, class of all metric spaces, von Neumann-Bernays-Gödel axioms, isometric embedding of a bounded metric space, generic metric space. 
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     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {Isometric embeddings of bounded metric spaces in the {Gromov-Hausdorff} class},
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A. O. Ivanov; A. A. Tuzhilin. Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class. Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1400-1414. http://geodesic.mathdoc.fr/item/SM_2022_213_10_a2/