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Theorems · Theorem · general topology

Dilation.injective

∀ {β : Type u_2} {F : Type u_4} [inst : PseudoEMetricSpace β] {α : Type u_5} [inst_1 : EMetricSpace α]
  [inst_2 : FunLike F α β] [DilationClass F α β] (f : F), Function.Injective ⇑f

A dilation from an emetric space is injective

Defined in
Mathlib.Topology.MetricSpace.Dilation
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Foundations
Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpaceEMetricSpaceFunLikeDilationClass
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DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEMetricSpace · cited by 242EMetricSpaceDilationClass · cited by 41DilationClassAntilipschitzWith.injective · cited by 8AntilipschitzWith.injecti…Dilation.antilipschitz · cited by 6Dilation.antilipschitzDilation.injectiveCITED BYCITES

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