Theorems · Theorem · general topology
Metric.inseparable_iff
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α}, Inseparable x y ↔ dist x y = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NNDist.nndistproof · cited by 235
- Inseparablestatement · cited by 160
- NNReal.coe_eq_zeroproof · cited by 11
- dist_nndistproof · cited by 10
- Metric.inseparable_iff_nndistproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- inseparable_zero_iff_normproof · cited by 1
- Inseparable.dist_eq_zeroproof · cited by 1
- Metric.toGlue_commuteproof · cited by 0
- Metric.toInductiveLimit_commuteproof · cited by 0
- SeparationQuotient.apply_eq_apply_of_inseparableproof · cited by 0
- inseparable_one_iff_normproof · cited by 0