Theorems · Theorem · general topology
Metric.cthickening_subset_of_subset
∀ {α : Type u} [inst : PseudoEMetricSpace α] (δ : ℝ) {E₁ E₂ : Set α},
E₁ ⊆ E₂ → Metric.cthickening δ E₁ ⊆ Metric.cthickening δ E₂The closed thickening Metric.cthickening δ E with a fixed thickening radius δ is
an increasing function of the subset E.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 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
- le_transproof · cited by 985
- Metric.cthickeningstatement and proof · cited by 113
- Metric.infEDist_antiproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Metric.closedBall_subset_cthickeningproof · cited by 6