What type of study is this?

This is a Quantitative Study study.

September 29, 2025Open Access

Calculating Gromov-Hausdorff distance by means of asymptotic dimension

View Full Paper

Ask AI

Bookmark

Gromov-Hausdorff distance equals Hausdorff distance between specific metric spaces, showing a fundamental relationship.
Calculating this distance between $ ext{R}^2$ and $ ext{Z}^2$ reveals their intrinsic geometric properties.
The approach utilizes asymptotic dimension, a key concept in understanding the structure of the spaces involved.
Implications of these findings suggest further exploration in unbounded metric spaces and their geometrical characteristics.

Implication

Application of asymptotic dimension determines Gromov-Hausdorff distance in metric spaces, suggesting new connections.

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: dGH(R², Z²) = dH(R², Z²).

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

I. N. Mikhailov (2025) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd11022 https://doi.org/10.48550/arxiv.2505.18158

View Full Paper

Ask AI

Bookmark

Implication

Application of asymptotic dimension determines Gromov-Hausdorff distance in metric spaces, suggesting new connections.

Calculating Gromov-Hausdorff distance by means of asymptotic dimension

Key Points

Implication

Abstract

Discussion

Cite This Study

Calculating Gromov-Hausdorff distance by means of asymptotic dimension

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading