Theorems · Definition · general topology
Set.infsep
{α : Type u_1} → [EDist α] → Set α → ℝThe "infimum separation" of a set with an edist function.
- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 127 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.
Cites5
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
- ENNReal.toRealproof · cited by 859
- EDiststatement and proof · cited by 91
- Set.einfsepproof · cited by 47
Cited by35
Results whose statement or proof uses this declaration.
- Set.Subsingleton.infsep_zerostatement · cited by 8
- Set.Nontrivial.le_infsep_iffstatement · cited by 6
- Set.infsep_pos_iff_nontrivial_of_finitestatement · cited by 2
- Set.infsep_zerostatement · cited by 2
- Set.infsep_zero_iff_subsingleton_of_finitestatement · cited by 2
- Set.Nontrivial.infsep_of_fintypestatement · cited by 2
- Finset.coe_infsepstatement and proof · cited by 2
- Set.infsep_eq_iInfstatement and proof · cited by 1
- Set.infsep_le_dist_of_memstatement · cited by 1
- Set.infsep_of_fintypestatement and proof · cited by 1
- Set.infsep_pair_eq_toRealstatement and proof · cited by 1
- Set.infsep_posstatement · cited by 1