Local Geometry of the Gromov–Hausdorff Metric Space and Totally Asymmetric Finite Metric Spaces

In the present paper, we investigate structure of metric space M compact spaces considered up to an isometry and endowed with Gromov–Hausdorff in a neighborhood finite space, whose group is trivial. It shown that sufficiently small ball subspace consisting same number points centered at such isometric corresponding ?N norm |(x1, . , xN)| = \( \underset{i}{\max}\left|{x}_i\right| \). Also embedding into asymmetric constructed.