论文标题
在紧凑型公制空间的空间中收敛
Convergence in the space of compact labeled metric spaces
论文作者
论文摘要
标记的度量空间正在直观地讲一个度量空间，并将一组特殊的点理解为空间的几何边界。我们研究了最近引入的Gromov-Hausdorff距离的基本特性，Gromov-Hausdorff距离是经典的Gromov-Hausdorff距离的扩展，该距离衡量了两个标记的度量标准空间的接近程度。 我们提供了一个结果的工具箱，以表征标有Gromov-Hausdorff距离的收敛性。我们获得了标记的度量空间空间和空间子集的预校准表征的完整结果。结果将应用于标记的度量空间环境中的旅行时间反问题。
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff distance, an extension of the classical Gromov-Hausdorff distance, which measures how close two labeled metric spaces are. We provide a toolbox of results characterizing convergence in the labeled Gromov-Hausdorff distance. We obtain a completeness result for the space of labeled metric spaces and precompactness characterizations for subsets of the space. The results are applied to travel time inverse problems in a labeled metric space context.
