Theorems · Theorem · general topology
Metric.ediam_thickening_le
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} (ε : NNReal),
Metric.ediam (Metric.thickening (↑ε) s) ≤ Metric.ediam s + 2 * ↑ε- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites12
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 · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- Metric.ediamstatement · cited by 159
- Metric.thickeningstatement · cited by 130
- Metric.ediam_monoproof · cited by 14
- Metric.thickening_subset_cthickeningproof · cited by 12
- Metric.ediam_cthickening_leproof · cited by 2
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