We study the geometry of the metric space of compact subsets of considered up to an orientation-preserving motion. We show that, in the optimal position of a pair of compact sets (for which the Hausdorff distance between the sets cannot be decreased), one of which is a singleton, this point is at the Chebyshev centre of the other. For orientedly similar compacta we evaluate the Euclidean Gromov-Hausdorff distance between them and prove that, in the optimal position, the Chebyshev centres of these compacta coincide. We show that every three-point metric space can be embedded isometrically in the space of compacta under consideration. We prove that, for a pair of optimally positioned compacta all compacta that lie in between in the sense of the Hausdorff metric also lie in between in the sense of the Euclidean Gromov-Hausdorff metric. For an arbitrary -point boundary formed by compact sets of a set that are neighbourhoods of segments, the Steiner point realizes the minimal filling and also belongs to the set .

Bibliography: 14 titles.

我们研究紧致子集的度量空间的几何 考虑到保持方向的运动。我们证明，在一对紧集的最优位置（对于该集合之间的 Hausdorff 距离不能减小），其中一个是单例，这个点在另一个的 Chebyshev 中心。对于定向相似的致密体，我们评估它们之间的欧几里得 Gromov-Hausdorff 距离，并证明在最佳位置，这些致密体的切比雪夫中心重合。我们表明，每个三点度量空间都可以等距嵌入到所考虑的紧凑空间中。我们证明，对于一对最佳定位的压缩，在 Hausdorff 度量的意义上位于两者之间的所有压缩也在欧几里得 Gromov-Hausdorff 度量的意义上位于两者之间。对于任意-点边界是由段的邻域的一个集合的紧集合形成的，Steiner点实现了最小填充并且也属于该集合。

参考书目：14个标题。