Theorems · Theorem · general topology
Metric.thickening_eq_biUnion_ball
∀ {X : Type u} [inst : PseudoMetricSpace X] {δ : ℝ} {E : Set X}, Metric.thickening δ E = ⋃ x ∈ E, Metric.ball x δThe (open) δ-thickening Metric.thickening δ E of a subset E in a metric space equals the
union of balls of radius δ centered at points of E.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- Metric.thickeningstatement and proof · cited by 130
- Metric.mem_thickening_iffproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- add_ball_zeroproof · cited by 4
- mul_ball_oneproof · cited by 3
- mem_approxOrderOf_iffproof · cited by 2
- mem_approx_add_orderOf_iffproof · cited by 2
- approxAddOrderOf.vadd_eq_of_mul_dvdproof · cited by 1
- approxAddOrderOf.vadd_subset_of_coprimeproof · cited by 1
- approxOrderOf.smul_eq_of_mul_dvdproof · cited by 0
- approxOrderOf.smul_subset_of_coprimeproof · cited by 0