Metric completions, the Heine-Borel property, and approachability
Metric completions, the Heine-Borel property, and approachability
Abstract 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 …