Theorems · Theorem · general topology
Metric.ball_subset_thickening
∀ {X : Type u} [inst : PseudoMetricSpace X] {x : X} {E : Set X},
x ∈ E → ∀ (δ : ℝ), Metric.ball x δ ⊆ Metric.thickening δ E- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 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.
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement and proof · cited by 735
- Set.Subset.transproof · cited by 218
- Set.singleton_subset_iffproof · cited by 206
- Metric.thickeningstatement · cited by 130
- Metric.thickening_singletonproof · cited by 11
- Metric.thickening_subset_of_subsetproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- approxAddOrderOf.image_nsmul_subsetproof · cited by 1
- approxAddOrderOf.image_nsmul_subset_of_coprimeproof · cited by 1
- approxOrderOf.image_pow_subsetproof · cited by 0
- approxOrderOf.image_pow_subset_of_coprimeproof · cited by 0