If the Hausdorff hyperspace is complete, its closed subspace of singletons is complete. Since that subspace is isometric to the original metric space, the original space is complete as well.

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  1. Closed singleton embedding in a Hausdorff hyperspace
  2. Hausdorff distance
  3. Metric space
  4. Topological analysis
  5. Analysis
  6. Area of mathematics
  7. Mathematics
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