Theorems · Theorem · general topology
Dilation.ediam_range
∀ {α : Type u_1} {β : Type u_2} {F : Type u_4} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
[inst_2 : FunLike F α β] [inst_3 : DilationClass F α β] (f : F),
Metric.ediam (Set.range ⇑f) = ↑(Dilation.ratio f) * Metric.ediam Set.univA dilation scales the diameter of the range by ratio f.
- Defined in
- Mathlib.Topology.MetricSpace.Dilation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- ENNRealstatement · cited by 9,879
- Set.rangestatement · cited by 4,705
- Set.univstatement and proof · cited by 3,945
- FunLikestatement and proof · cited by 2,560
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- Set.image_univproof · cited by 322
- Metric.ediamstatement and proof · cited by 159
- Dilation.ratiostatement and proof · cited by 43
- DilationClassstatement and proof · cited by 41
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