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arXiv · 2407.01388

Gromov-Hausdorff distances between normed spaces

I. N. Mikhailov
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Abstract

In the present paper we study the original Gromov-Hausdorff distance between real normed spaces. In the first part of the paper we prove that two finite-dimensional real normed spaces on a finite Gromov-Hausdorff distance are isometric to each other. We then study the properties of finite point sets in finite-dimensional normed spaces whose cardinalities exceed the equilateral dimension of an ambient space. By means of the obtained results we prove the following enhancement of the aforementioned theorem: every finite-dimensional normed space lies on an infinite Gromov-Hausdorff distance from all other non-isometric normed spaces.

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I. N. Mikhailov. 2024-07-01. Gromov-Hausdorff distances between normed spaces. https://arxiv.org/abs/2407.01388

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