Theorems · Definition · general topology
TopologicalSpace.completelyMetrizableMetric
(X : Type u_3) → [inst : TopologicalSpace X] → [h : TopologicalSpace.IsCompletelyMetrizableSpace X] → MetricSpace X
Construct on a completely metrizable space a metric (compatible with the topology) which is complete.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MetricSpacestatement · cited by 1,684
- TopologicalSpace.IsCompletelyMetrizableSpacestatement and proof · cited by 7
- TopologicalSpace.IsCompletelyMetrizableSpace.completeproof · cited by 1
- MetricSpace.replaceTopologyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.complete_completelyMetrizableMetricstatement and proof · cited by 0