Theorems · Theorem · general topology
Metric.closedBall_subset_cthickening
∀ {α : Type u_2} [inst : PseudoMetricSpace α] {x : α} {E : Set α},
x ∈ E → ∀ (δ : ℝ), Metric.closedBall x δ ⊆ Metric.cthickening δ EThe closed ball of radius δ centered at a point of E is included in the closed
thickening of E.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 151 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
- LE.le.transproof · cited by 3,151
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Metric.cthickeningstatement · cited by 113
- Metric.cthickening_subset_of_subsetproof · cited by 1
- Metric.closedBall_subset_cthickening_singletonproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- TendstoLocallyUniformlyOn.derivproof · cited by 3
- IsCompact.cthickening_eq_biUnion_closedBallproof · cited by 2
- TendstoUniformlyOn.cderivproof · cited by 1
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- Metric.cthickening_eq_biUnion_closedBallproof · cited by 1
- Complex.tendstoUniformlyOn_deriv_of_cthickening_subsetproof · cited by 1