Theorems · Theorem · general topology
Set.infsep_pos_iff_nontrivial_of_finite
∀ {α : Type u_1} [inst : MetricSpace α] {s : Set α} [Finite ↑s], 0 < s.infsep ↔ s.Nontrivial- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Elemstatement and proof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- MetricSpacestatement and proof · cited by 1,684
- Set.Nontrivialstatement and proof · cited by 145
- Set.einfsepproof · cited by 47
- Set.infsepstatement · cited by 35
- Set.einfsep_pos_of_finiteproof · cited by 4
- Set.infsep_posproof · cited by 1
- Set.einfsep_lt_top_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.infsep_pos_iff_nontrivialproof · cited by 0
- Set.Finite.infsep_pos_iff_nontrivialproof · cited by 0