Theorems · Theorem · general topology
Metric.mem_cthickening_of_edist_le
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x y : α) (δ : ℝ) (E : Set α),
y ∈ E → edist x y ≤ ENNReal.ofReal δ → x ∈ Metric.cthickening δ 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.
Cites9
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
- ENNRealstatement · cited by 9,879
- LE.le.transproof · cited by 3,151
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealstatement and proof · cited by 863
- EDist.ediststatement and proof · cited by 735
- Metric.cthickeningstatement · cited by 113
- Metric.infEDist_le_edist_of_memproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Metric.mem_cthickening_of_dist_leproof · cited by 2