2019/06/23 by Grigor'ev, D. S., Ivanov, A. O., Tuzhilin, A. A.
#51G99 #53C23 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1906.09644
Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whose non-zero distances are the same are studied. The corresponding calculations essentially use geometry of partitions of these spaces. In the finite case, it gives the lengths of minimal spanning trees. A similar theory for compact metric spaces was worked out previously. In the present paper we generalize those results to any bounded metric space, and also, we simplify some proofs.