English

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

Metric Geometry 2025-08-12 v2 General Topology

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.

Keywords

Cite

@article{arxiv.2507.07449,
  title  = {A sequence of compact metric spaces and an isometric embedding into the Gromov-Hausdorff space},
  author = {Takuma Byakuno},
  journal= {arXiv preprint arXiv:2507.07449},
  year   = {2025}
}