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.
Bibliographical notePublisher Copyright:
© 2020 Vladimir Kanovei et al., published by De Gruyter 2020.
- Heine-Borel property
- metric completion
- nonstandard hull
- universal cover