Theorems · Theorem · general topology
Set.Nontrivial.einfsep_ne_top
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α}, s.Nontrivial → s.einfsep ≠ ⊤- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 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.
Cites7
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.Nontrivialstatement and proof · cited by 145
- Set.einfsepstatement and proof · cited by 47
- Set.subsingleton_of_einfsep_eq_topproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Set.Nontrivial.le_infsep_iffproof · cited by 6
- Set.Nontrivial.einfsep_lt_topproof · cited by 1
- Set.Nontrivial.infsep_antiproof · cited by 0
- Set.einfsep_ne_top_iffproof · cited by 0