Theorems · Theorem · general topology
Metric.closure_eq_iInter_thickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] (E : Set α), closure E = ⋂ δ, ⋂ (_ : 0 < δ), Metric.thickening δ EThe closure of a set equals the intersection of its (open) thickenings of positive radii.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 3 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.
Cites9
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
- Eq.geproof · cited by 375
- Metric.thickeningstatement and proof · cited by 130
- Metric.cthickening_zeroproof · cited by 8
- Metric.cthickening_eq_iInter_thickeningproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- ae_eq_zero_of_integral_contMDiff_smul_eq_zeroproof · cited by 3
- tendsto_measure_thickeningproof · cited by 2
- IsClopen.of_thickening_subset_selfproof · cited by 2