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Extendability of Metric Segments in Gromov--Hausdorff Distance

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arxiv 2009.00458 v1 pith:TZW5IYNH submitted 2020-08-26 math.MG math.FAmath.GN

S.I.Borzov , A.O.Ivanov , A.A.Tuzhilin This is my paper · ORCID
classification math.MGmath.FAmath.GN
keywords considereddistancemetricsegmentsclassgromov-hausdorffbesidesbeyond
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer

    math.MG 2025-05 conditional novelty 6.0 of 10

    The Gromov-Hausdorff distance between the cloud of bounded metric spaces and the cloud containing the real line is infinite, and a criterion for such infinite cloud distances is proved.

  2. Ultrametric spaces and clouds

    math.MG 2025-01 conditional novelty 5.0 of 10

    The ultrametrization map U is 1-Lipschitz on all metric spaces, preserves products with dotted connected spaces, and forces mutual exclusion of ultrametric and dotted connected spaces in unbounded clouds.

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