Theorems · Theorem · general topology
Set.infsep_zero
∀ {α : Type u_1} [inst : EDist α] {s : Set α}, s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ⊤- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 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.
Cites8
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 and proof · 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
- ENNReal.toReal_eq_zero_iffproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Set.Subsingleton.infsep_zeroproof · cited by 8
- Set.infsep_zero_iff_subsingleton_of_finiteproof · cited by 2