2019/06/25 by Alexander Ivanov, Ivanov, Alexander, Alexei Tuzhilin +1
Mathematics · #51G99 #53C23 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1906.10574
openalex publication_date 2019/06/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In the present paper the following Generalized Borsuk Problem is studied: Can\na given bounded metric space X be partitioned into a given number m\n(probably an infinite one) of subsets, each of which has a smaller diameter\nthan X? We give a complete answer to this question in terms of the\nGromov-Hausdorff distance from X to a simplex of cardinality m and having a\ndiameter less than X. Here a simplex is a metric space, all whose non-zero\ndistances are the same.\n