Theorems · Theorem · general topology
Metric.thickening_subset_of_subset
∀ {α : Type u} [inst : PseudoEMetricSpace α] (δ : ℝ) {E₁ E₂ : Set α},
E₁ ⊆ E₂ → Metric.thickening δ E₁ ⊆ Metric.thickening δ E₂The (open) thickening Metric.thickening δ E with a fixed thickening radius δ is
an increasing function of the subset E.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 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.
Cites6
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
- lt_of_le_of_ltproof · cited by 432
- Metric.thickeningstatement and proof · cited by 130
- Metric.infEDist_antiproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Metric.ball_subset_thickeningproof · cited by 4
- MeasureTheory.tendsto_integral_meas_thickening_leproof · cited by 1
- IsCompact.exists_thickening_image_subsetproof · cited by 0