Theorems · Theorem · general topology
Metric.subset_compl_thickening_compl_thickening_self
∀ {α : Type u} [inst : PseudoEMetricSpace α] (δ : ℝ) (E : Set α), E ⊆ (Metric.thickening δ (Metric.thickening δ E)ᶜ)ᶜAny set is contained in the complement of the δ-thickening of the complement of its δ-thickening.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 2 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.
Cites12
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
- Set.ofPredproof · cited by 6,101
- Compl.complstatement and proof · cited by 2,925
- PseudoEMetricSpacestatement and proof · cited by 1,536
- le_transproof · cited by 985
- ENNReal.ofRealproof · cited by 863
- Metric.infEDistproof · cited by 147
- Metric.thickeningstatement · cited by 130
- PseudoEMetricSpace.edist_commproof · cited by 52
- Metric.infEDist_le_edist_of_memproof · cited by 13
- Metric.le_infEDistproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.levyProkhorovEDist_le_of_forall_leproof · cited by 1
- Metric.thickening_compl_thickening_self_subset_complproof · cited by 0