Theorems · Definition · general topology
TopologicalSpace.metrizableSpaceMetric
(X : Type u_2) → [inst : TopologicalSpace X] → [TopologicalSpace.MetrizableSpace X] → MetricSpace X
Construct on a metrizable space a metric compatible with the topology.
- Defined in
- Mathlib.Topology.Metrizable.Uniformity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.MetrizableSpacestatement and proof · cited by 39
- MetricSpace.ofT0PseudoMetricSpaceproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ae_eq_zero_of_integral_contMDiff_smul_eq_zeroproof · cited by 3