论文标题
Gromov-Hausdorff距离的度量段的可扩展性
Extendability of Metric Segments in Gromov--Hausdorff Distance
论文作者
论文摘要
在本文中，研究了所有被认为是等轴测图的公制空间的Gromov-Hausdorff距离的几何形状。对于这个类别，连续曲线及其长度被定义，并且表明Gromov-Hausdorff的距离是固有的。此外，还考虑了度量段，即，位于两个给定的点之间的点类别，并且考虑了此类段以外的末端段的扩展问题。
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.
