Theorems · Theorem · general topology
Set.subsingleton_of_einfsep_eq_top
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α}, s.einfsep = ⊤ → s.Subsingleton- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 147 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- PseudoMetricSpacestatement and proof · cited by 1,550
- Set.Subsingletonstatement · cited by 276
- of_not_notproof · cited by 51
- Set.einfsepstatement and proof · cited by 47
- edist_ne_topproof · cited by 17
- Set.einfsep_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Set.Nontrivial.einfsep_ne_topproof · cited by 4
- Set.einfsep_eq_top_iffproof · cited by 1