Theorems · Theorem · general topology
Metric.thickening_empty
∀ {α : Type u} [inst : PseudoEMetricSpace α] (δ : ℝ), Metric.thickening δ ∅ = ∅The (open) thickening of the empty set is empty.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealproof · cited by 863
- Metric.thickeningstatement · cited by 130
- Metric.infEDist_emptyproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Metric.thickening_thickening_subsetproof · cited by 4
- Bornology.IsBounded.thickeningproof · cited by 1
- Metric.thickening_eq_empty_iff_of_posproof · cited by 1
- IsCompact.exists_thickening_image_subsetproof · cited by 0