Theorems · Theorem · general topology

Dilation.mapsTo_closedEBall

∀ {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) (x : α) (r' : ENNReal),
  Set.MapsTo (⇑f) (Metric.closedEBall x r') (Metric.closedEBall (f x) (↑(Dilation.ratio f) * r'))

A dilation maps closed balls to closed balls and scales the radius by ratio f.

Defined in

Mathlib.Topology.MetricSpace.Dilation

Cited by

1 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpaceFunLikeDilationClass