论文标题
公制完成，海因 - 机器人属性和可易到的性能
Metric completions, the Heine-Borel property, and approachability
论文作者
论文摘要
我们表明，带穿刺的平面的度量通用盖产生了一个非标准船体的示例，该命中符合度量空间的度量完成。正如Do Carmo所提到的那样，无Xtendendsendible的Riemannian歧管可能是非完成的，但是在更广泛的度量空间类别中，它变得可扩展。我们简短地证明了公制空间m的Heine-borel特性的表征，因为缺乏 *m中的不可接受的有限点。
We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space. As mentioned by do Carmo, a nonextendible Riemannian manifold can be noncomplete, but in the broader category of metric spaces it becomes extendible. We give a short proof of a characterisation of the Heine-Borel property of the metric completion of a metric space M in terms of the absence of inapproachable finite points in *M.
