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. The paper proves that all clouds are proper classes. The Gromov – Hausdorff distance is defined for clouds analogous to the case of metric spaces. The paper shows that under certain limitations 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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