Extendability of Metric Segments in Gromov--Hausdorff Distance
Metric Geometry
2020-09-02 v1 Functional Analysis
General Topology
Abstract
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.
Keywords
Cite
@article{arxiv.2009.00458,
title = {Extendability of Metric Segments in Gromov--Hausdorff Distance},
author = {S. I. Borzov and A. O. Ivanov and A. A. Tuzhilin},
journal= {arXiv preprint arXiv:2009.00458},
year = {2020}
}
Comments
19 pages