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Theorems · Theorem · general topology

Dilation.toContinuous

∀ {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] [DilationClass F α β] (f : F), Continuous ⇑f

A dilation is continuous.

Defined in
Mathlib.Topology.MetricSpace.Dilation
Cited by
0 results in Mathlib
Foundations
Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpaceFunLikeDilationClass
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Around this declaration

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DFunLike.coe · cited by 62936DFunLike.coeContinuous · cited by 2592ContinuousFunLike · cited by 2560FunLikePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceDilationClass · cited by 41DilationClassLipschitzWith.continuous · cited by 30LipschitzWith.continuousDilation.lipschitz · cited by 6Dilation.lipschitzDilation.toContinuousCITED BYCITES

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