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PreprintCC BY 4.0arXiv

An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space

  • Takuma Byakuno
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Abstract

The Gromov-Hausdorff space is a certain metric space induced by the Gromov-Hausdorff convergence, and we study an isometric embedding into this space. While the subspace of non-negative real numbers in the Euclidean space admits an isometric embedding, we prove that the subspace of ℓ∞ consisting of non-increasing sequences with non-negative terms can be isometrically embedded into the Gromov-Hausdorff space.

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Cite

BibTeXRIS
BibTeX
@misc{byakuno2026isometric,
  title = {{An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space}},
  author = {Takuma Byakuno},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34727},
  eprint = {2610.34727},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34727},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space
AU  - Takuma Byakuno
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34727
UR  - https://arxiv.org/abs/2610.34727
AB  - The Gromov-Hausdorff space is a certain metric space induced by the Gromov-Hausdorff convergence, and we study an isometric embedding into this space. While the subspace of non-negative real numbers in the Euclidean space admits an isometric embedding, we prove that the subspace of ℓ^∞ consisting of non-increasing sequences with non-negative terms can be isometrically embedded into the Gromov-Hausdorff space.
ER  -