论文标题
Gromov-Hausdorff班级的云层：它们的完整性和中心
Clouds in Gromov-Hausdorff Class: their completeness and centers
论文作者
论文摘要
我们考虑了与gromov-hausdorff距离的所有公制空间的适当类别。它的最大子类，由彼此有限距离的空间组成，我们称为云。将公制空间中的所有距离乘以相同的正实数，我们获得了Gromov-Hausdorff类的相似性转换。在我们以前的工作中，我们观察到有这样的转变，有些云可以跳到其他云中。为了表征这种现象，我们研究了相似性作用的稳定器。在本文中，我们证明每个具有非平地稳定器的云都有一个中心，即，稳定器的所有相似性都在零距离下产生一个新空间。此外，该中心是唯一的零距离。证明基于云完整定理。
We consider the proper class of all metric spaces endowed with the Gromov--Hausdorff distance. Its maximal subclasses, consisting of the spaces on finite distance from each other, we call clouds. Multiplying all distances in a metric space by the same positive real number, we obtain a similarity transformation of the Gromov--Hausdorff class. In our previous work, we observed that with such a transformation, some clouds can jump to others. To characterize the phenomenon, we studied the stabilizers of the similarity action. In this paper, we prove that every cloud with a nontrivial stabilizer has a center, i.e., a metric space for which all similarities from the stabilizer generate a new space at zero distance. Moreover, the center is unique modulo zero distance. The proof is based on the cloud completeness theorem.
