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Closed-subspace completeness theorem

A closed subspace of a complete metric space is complete. A Cauchy sequence in the subspace converges in the ambient space, and closedness keeps its limit in the subspace.

Ancestors (7)

  1. Complete metric space
  2. Metric space
  3. Topological analysis
  4. Analysis
  5. Area of mathematics
  6. Mathematics
  7. Home

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