Theorems · Definition · general topology
TopologicalSpace.completelyPseudoMetrizableMetric
(X : Type u_3) → [inst : TopologicalSpace X] → [h : TopologicalSpace.IsCompletelyPseudoMetrizableSpace X] → PseudoMetricSpace X
Construct on a completely pseudometrizable space a pseudometric (compatible with the topology) which is complete.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 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
- PseudoMetricSpacestatement · cited by 1,550
- TopologicalSpace.IsCompletelyPseudoMetrizableSpacestatement and proof · cited by 23
- TopologicalSpace.IsCompletelyPseudoMetrizableSpace.completeproof · cited by 1
- PseudoMetricSpace.replaceTopologyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.complete_completelyPseudoMetrizableMetricstatement and proof · cited by 0