论文标题
Gromov- Hausdorff类的公制段
Metric Segments in Gromov--Hausdorff class
论文作者
论文摘要
我们研究所有公制空间中的度量段的属性，该级别被认为是gromov-hausdorff距离的等轴测图。在所有紧凑型公制空间的等轴测类别上，Gromov-Hausdorff距离是度量标准。度量段是一个由两个给定标准段组成的类。作者：von Neumann-Bernays-Gödel（NBG）公理集理论，适当的类是“怪物收集”，例如，所有基本集合的集合。我们证明，如果该段至少在距离段端点的正距离处包含至少一个度量空间，那么所有指标空间的适当类等轴测类别中的任何度量段都是适当的类。此外，我们表明，非分类度量段限制了紧凑的度量空间是一个非紧凑的集合。
We study properties of metric segments in the class of all metric spaces considered up to an isometry, endowed with Gromov--Hausdorff distance. On the isometry classes of all compact metric spaces, the Gromov-Hausdorff distance is a metric. A metric segment is a class that consists of points lying between two given ones. By von Neumann--Bernays--Gödel (NBG) axiomatic set theory, a proper class is a "monster collection", e.g., the collection of all cardinal sets. We prove that any metric segment in the proper class of isometry classes of all metric spaces with the Gromov-Hausdorff distance is a proper class if the segment contains at least one metric space at positive distances from the segment endpoints. In addition, we show that the restriction of a non-degenerated metric segment to compact metric spaces is a non-compact set.
