Calculating Gromov-Hausdorff distance by means of asymptotic dimension

2025/05/01 by Mikhailov, Ivan N.
#51F99 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2505.18158

Abstract

In this paper, we apply the concept of asymptotic dimension to calculating Gromov-Hausdorff distances between some unbounded metric spaces. For example, we show that the Gromov--Hausdorff between ℝ² with the Euclidean metric and ℤ² equals the Hausdorff distance between them: d_GH(ℝ², ℤ²) = d_H(ℝ², ℤ²).

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