A sequence of compact metric spaces and an isometric embedding into the Gromov-Hausdorff space

TL;DR

The paper demonstrates that a sequence of compact metric spaces can be isometrically embedded into the Gromov-Hausdorff space using a convergent series with positive terms, expanding understanding of the space's structure.

Contribution

It introduces a method to embed a sequence of bounded subspaces of the Gromov-Hausdorff space into the space itself, based on a convergent series.

Findings

Isometric embedding of a sequence of compact metric spaces achieved

Embedding relies on a convergent series with positive terms

Expands understanding of Gromov-Hausdorff space structure

Abstract

For a convergent series with positive terms, we prove that the $\ell^\infty$ product space of bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space, where each subspace consists of compact metric spaces with the diameter less than or equal to the term.