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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arXiv · 2610.34727

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 $\ell^\infty$ consisting of non-increasing sequences with non-negative terms can be isometrically embedded into the Gromov-Hausdorff space.

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BibTeX RIS

Takuma Byakuno. 2026-10-26. An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space. https://arxiv.org/abs/2610.34727

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