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In this paper geometry of Gromov-Hausdorff distance on the class of allmetric spaces considered up to an isometry is investigated. For this classcontinuous curves and their lengths are defined, and it is shown that theGromov-Hausdorff distance is intrinsic. Besides, metric segments areconsidered, i.e., the classes of points lying between two given ones, and anextension problem of such segments beyond their end-points is considered.

Extendability of Metric Segments in Gromov--Hausdorff Distance