论文标题
指标和指标空间的插值
An interpolation of metrics and spaces of metrics
论文作者
论文摘要
作为对Hausdorff的扩展定理的概括，我们证明了在可倾斜空间的封闭子集上定义的一个指标家族的插值定理。作为应用程序，我们研究了指标模量空间的子集的典型性。我们观察到，所有指标中出现属性的各种指标集是在可元空间上指标空间中可数开放子集的密集交集。例如，我们的研究适用于所有非倍增指标的集合以及所有非均匀断开指标的集合。
As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli spaces of metrics. We observe that various sets of all metrics with properties appearing in metric geometry are dense intersections of countable open subsets in spaces of metrics on metrizable spaces. For instance, our study is applicable to the set of all non-doubling metrics and the set of all non-uniformly disconnected metrics.
