Theorems · Theorem · general topology
Disjoint.exists_thickenings
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
Disjoint s t → IsCompact s → IsClosed t → ∃ δ, 0 < δ ∧ Disjoint (Metric.thickening δ s) (Metric.thickening δ t)- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 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.
Cites27
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
- ENNRealproof · cited by 9,879
- NNRealproof · cited by 4,310
- Disjointstatement and proof · cited by 2,201
- LT.lt.leproof · cited by 2,189
- IsClosedstatement and proof · cited by 1,639
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- ENNReal.ofRealproof · cited by 863
Cited by1
Results whose statement or proof uses this declaration.
- Disjoint.exists_cthickeningsproof · cited by 1