Theorems · Theorem · general topology
Set.Finite.infsep_pos_iff_nontrivial
∀ {α : Type u_1} [inst : MetricSpace α] {s : Set α}, s.Finite → (0 < s.infsep ↔ s.Nontrivial)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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
- Set.Finitestatement and proof · cited by 1,814
- MetricSpacestatement and proof · cited by 1,684
- Set.Nontrivialstatement · cited by 145
- Set.infsepstatement · cited by 35
- Set.infsep_pos_iff_nontrivial_of_finiteproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.