Theorems · Definition · general topology
EMetricSpace.ofT0PseudoEMetricSpace
(α : Type u_2) → [inst : PseudoEMetricSpace α] → [T0Space α] → EMetricSpace α
If a PseudoEMetricSpace is a T₀ space, then it is an EMetricSpace.
- Defined in
- Mathlib.Topology.EMetricSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpaceT0Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EMetricSpacestatement · cited by 242
- T0Spacestatement and proof · cited by 179
Cited by1
Results whose statement or proof uses this declaration.
- EMetricSpace.ofRiemannianMetricproof · cited by 0