Calculating Gromov-Hausdorff distance by means of asymptotic dimension

Key Points

• 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.