Theorems · Theorem · general topology

Isometry.mapsTo_closedEBall

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  Isometry f → ∀ (x : α) (r : ENNReal), Set.MapsTo f (Metric.closedEBall x r) (Metric.closedEBall (f x) r)

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

1 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace