Theorems · Theorem · general topology
Metric.ediam_cthickening_le
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} (ε : NNReal),
Metric.ediam (Metric.cthickening (↑ε) s) ≤ Metric.ediam s + 2 * ↑ε- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 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.
Cites26
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
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- LE.le.trans_ltproof · cited by 795
- EDist.edistproof · cited by 735
- add_le_addproof · cited by 666
Cited by2
Results whose statement or proof uses this declaration.
- Metric.diam_cthickening_leproof · cited by 1
- Metric.ediam_thickening_leproof · cited by 0