Theorems · Theorem · general topology
Metric.closure_eq_iInter_cthickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] (E : Set α), closure E = ⋂ δ, ⋂ (_ : 0 < δ), Metric.cthickening δ EThe closure of a set equals the intersection of its closed thickenings of positive radii.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 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.
Cites8
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
- closurestatement · cited by 1,254
- Set.iInterstatement and proof · cited by 1,084
- Metric.cthickeningstatement and proof · cited by 113
- Metric.cthickening_zeroproof · cited by 8
- Metric.cthickening_eq_iInter_cthickeningproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_measure_cthickeningproof · cited by 1