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arXiv · 2505.23563

On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer

B. A. Nesterov
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Abstract

The paper studies the class of all metric spaces considered up to zero Gromov-Hausdorff distance between them. In this class, we examine clouds - classes of spaces situated at finite Gromov-Hausdorff distances from a reference space. We prove that all clouds are proper classes. The Gromov-Hausdorff distance is defined for clouds similarly with the case of that for metric spaces. A multiplicative group of transformations of clouds is defined which is called stabilizer. We show that under certain restrictions the distance between the cloud of bounded metric spaces and a cloud with a nontrivial stabilizer is finite. In particular, the distance between the cloud of bounded metric spaces and the cloud containing the real line is calculated.

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B. A. Nesterov. 2025-05-29. On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer. https://arxiv.org/abs/2505.23563

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