Theorems · Theorem · general topology
Metric.thickening_mono
∀ {α : Type u} [inst : PseudoEMetricSpace α] {δ₁ δ₂ : ℝ},
δ₁ ≤ δ₂ → ∀ (E : Set α), Metric.thickening δ₁ E ⊆ Metric.thickening δ₂ EThe (open) thickening Metric.thickening 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.thickeningstatement · cited by 130
- Set.preimage_monoproof · cited by 95
- ENNReal.ofReal_le_ofRealproof · cited by 61
- Set.Iio_subset_Iioproof · cited by 18
Cited by6
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
- MeasureTheory.meas_le_of_le_of_forall_le_meas_thickening_addproof · cited by 2
- Metric.cthickening_eq_iInter_thickening'proof · cited by 2
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- IsCompact.exists_thickening_image_subsetproof · cited by 0