Theorems · Theorem · general topology
Metric.cthickening_mono
∀ {α : Type u} [inst : PseudoEMetricSpace α] {δ₁ δ₂ : ℝ},
δ₁ ≤ δ₂ → ∀ (E : Set α), Metric.cthickening δ₁ E ⊆ Metric.cthickening δ₂ EThe closed thickening Metric.cthickening δ E of a fixed subset E is an increasing function
of the thickening radius δ.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 149 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.
Cites7
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
- Metric.cthickeningstatement · cited by 113
- Set.preimage_monoproof · cited by 95
- ENNReal.ofReal_le_ofRealproof · cited by 61
- Set.Iic_subset_Iicproof · cited by 25
Cited by6
Results whose statement or proof uses this declaration.
- Metric.closure_subset_cthickeningproof · cited by 4
- Metric.cthickening_eq_iInter_cthickening'proof · cited by 3
- blimsup_cthickening_ae_le_of_eventually_mul_leproof · cited by 1
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- Metric.thickening_subset_cthickening_of_leproof · cited by 1
- tendsto_measure_cthickeningproof · cited by 1