Theorems · Theorem · general topology
Set.infsep_pos
∀ {α : Type u_1} [inst : EDist α] {s : Set α}, 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ⊤- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 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.
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
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- EDiststatement and proof · cited by 91
- Set.einfsepstatement and proof · cited by 47
- Set.infsepstatement · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Set.infsep_pos_iff_nontrivial_of_finiteproof · cited by 2