Abstract
Optimal Connections Problem in the Gromov–Hausdorff space of metric compacta is investigated. To study Gromov–Hausdorff distances the technique of irreducible correspondences and relations with the finite-dimensional space with max-norm are used. As a result it is shown that the Steiner and the Gromov–Steiner ratios of the Gromov–Hausdorff space are equal to 1∕2, but the Steiner subratio is less than 1. Moreover, a smaller estimate for the Steiner subratio is obtained.
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