Theorems · Theorem · general topology
Set.nontrivial_of_einfsep_lt_top
∀ {α : Type u_1} [inst : EDist α] {s : Set α}, s.einfsep < ⊤ → s.Nontrivial- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 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.
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
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- EDist.edistproof · cited by 735
- Set.Nontrivialstatement · cited by 145
- EDiststatement and proof · cited by 91
- Set.einfsepstatement and proof · cited by 47
- Set.einfsep_lt_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.einfsep_lt_top_iffproof · cited by 1
- Set.nontrivial_of_einfsep_ne_topproof · cited by 1