Theorems · Theorem · general topology
Metric.thickening_eq_empty_iff_of_pos
∀ {α : Type u} [inst : PseudoEMetricSpace α] {ε : ℝ} {s : Set α}, 0 < ε → (Metric.thickening ε s = ∅ ↔ s = ∅)- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 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 and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.thickeningstatement and proof · cited by 130
- Metric.self_subset_thickeningproof · cited by 10
- Set.subset_eq_emptyproof · cited by 6
- Metric.thickening_emptyproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Metric.thickening_nonempty_iff_of_posproof · cited by 0