度量及其空间的插值
An interpolation of metrics and spaces of metrics
AI总结：
本文提出了一种度量及其空间的插值定理，并探讨了度量空间中子集的典型性，通过研究各种度量集合的稠密交集，展示了其在非倍度和非均匀断开度量中的应用。
摘要：
作为Hausdorff度量扩展定理的推广，我们证明了在可度量空间的闭子集上定义的一族度量的插值定理。作为应用，我们研究了度量空间中子集的典型性。我们观察到，各种具有出现在度量几何中性质的所有度量集合都是可度量空间中可数开子集的稠密交集。例如，我们的研究可应用于所有非倍度度量集合和所有非均匀断开度量集合。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
