Theorems · Theorem · general topology
Set.einfsep_lt_top
∀ {α : Type u_1} [inst : EDist α] {s : Set α}, s.einfsep < ⊤ ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y < ⊤- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EDist
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- EDist.ediststatement and proof · cited by 735
- EDiststatement and proof · cited by 91
- Set.einfsepstatement · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- Set.nontrivial_of_einfsep_lt_topproof · cited by 2