An Isometric Embedding of the $\ell^\infty$ product space of two bounded subspaces of the Gromov-Hausdorff Space into the Gromov-Hausdorff Space

TL;DR

This paper demonstrates that the $\, ext{ extlbrackdbl} ext{ extlbrackdbl} ext{ extrbrackdbl} ext{ extrbrackdbl}$ product space of two bounded subspaces of the Gromov-Hausdorff space can be embedded without distortion into the same space.

Contribution

It provides a new isometric embedding result for the $\, ext{ extlbrackdbl} ext{ extlbrackdbl} ext{ extrbrackdbl} ext{ extrbrackdbl}$ product space within the Gromov-Hausdorff space.

Findings

The $\, ext{ extlbrackdbl} ext{ extlbrackdbl} ext{ extrbrackdbl} ext{ extrbrackdbl}$ product space can be embedded isometrically.

Embedding preserves distances exactly.

The result applies to bounded subspaces of the Gromov-Hausdorff space.

Abstract

In this paper, we prove the $\ell^\infty$ product space of two bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space.