Theorems · Theorem · general topology

diam_smul

∀ {M : Type u} {X : Type w} [inst : PseudoMetricSpace X] [inst_1 : SMul M X] [IsIsometricSMul M X] (c : M) (s : Set X),
  Metric.diam (c • s) = Metric.diam s

Defined in: Mathlib.Topology.MetricSpace.IsometricSMul
Cited by: 0 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace SMul IsIsometricSMul

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Setstatement and proof · cited by 53,352
Realstatement · cited by 25,697
PseudoMetricSpacestatement and proof · cited by 1,550
Set.smulSetstatement · cited by 608
Metric.diamstatement · cited by 74
IsIsometricSMulstatement and proof · cited by 74
IsIsometricSMul.isometry_smulproof · cited by 10
Isometry.diam_imageproof · cited by 10

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