Theorems · Theorem · general topology
Metric.thickening_thickening_subset
∀ {α : Type u} [inst : PseudoEMetricSpace α] (ε δ : ℝ) (s : Set α),
Metric.thickening ε (Metric.thickening δ s) ⊆ Metric.thickening (ε + δ) sFor the equality, see thickening_thickening.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 151 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.
Cites13
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
- ENNReal.ofRealproof · cited by 863
- LE.le.trans_ltproof · cited by 795
- EDist.edistproof · cited by 735
- le_totalproof · cited by 294
- Metric.thickeningstatement and proof · cited by 130
- ENNReal.ofReal_addproof · cited by 26
- PseudoEMetricSpace.edist_triangleproof · cited by 24
- ENNReal.add_lt_addproof · cited by 13
- Metric.thickening_of_nonposproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- thickening_thickeningproof · cited by 2
- MeasureTheory.levyProkhorovEDist_triangleproof · cited by 1
- IsCompact.exists_thickening_image_subsetproof · cited by 0
- Metric.thickening_ballproof · cited by 0