The generalized Borsuk problem is solved by the criterion that a bounded metric space X admits an m-partition into smaller-diameter sets if and only if its Gromov-Hausdorff distance to an m-point simplex of smaller diameter is positive.
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New closed-form expression for Gromov-Hausdorff distance between a simplex and a bounded metric space (under cardinality condition), extended to exact distance with ultrametric spaces.
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Solution to Generalized Borsuk Problem in Terms of the Gromov-Hausdorff Distances to Simplexes
The generalized Borsuk problem is solved by the criterion that a bounded metric space X admits an m-partition into smaller-diameter sets if and only if its Gromov-Hausdorff distance to an m-point simplex of smaller diameter is positive.
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The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces
New closed-form expression for Gromov-Hausdorff distance between a simplex and a bounded metric space (under cardinality condition), extended to exact distance with ultrametric spaces.