Theorems · Theorem · general topology
Metric.thickening_of_nonpos
∀ {α : Type u} [inst : PseudoEMetricSpace α] {δ : ℝ}, δ ≤ 0 → ∀ (s : Set α), Metric.thickening δ s = ∅- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- bot_leproof · cited by 306
- LE.le.not_gtproof · cited by 189
- Eq.trans_leproof · cited by 155
- Metric.thickeningstatement · cited by 130
- Set.eq_empty_of_forall_notMemproof · cited by 21
- ENNReal.ofReal_of_nonposproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Metric.thickening_thickening_subsetproof · cited by 4
- Metric.cthickening_thickening_subsetproof · cited by 1
- Metric.frontier_thickening_disjointproof · cited by 1
- Metric.thickening_cthickening_subsetproof · cited by 0
- Metric.diam_thickening_leproof · cited by 0
- Metric.thickening_eq_empty_iffproof · cited by 0