2020/08/26 by S. I. Borzov, A. O. Ivanov, Borzov, S. I. +3 · 2 citations
Mathematics · #51F99 #53C23 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2009.00458
openalex publication_date 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper geometry of Gromov-Hausdorff distance on the class of all metric spaces considered up to an isometry is investigated. For this class continuous curves and their lengths are defined, and it is shown that the Gromov-Hausdorff distance is intrinsic. Besides, metric segments are considered, i.e., the classes of points lying between two given ones, and an extension problem of such segments beyond their end-points is considered.