Isometry.preimage_emetric_ball

Deprecated since 2026-01-24Use Isometry.preimage_eball instead.

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  Isometry f → ∀ (x : α) (r : ENNReal), f ⁻¹' Metric.eball (f x) r = Metric.eball x r

Alias of Isometry.preimage_eball.

Defined in: Mathlib.Topology.MetricSpace.Isometry
Cited by: 0 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoEMetricSpace PseudoEMetricSpace

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Setstatement · cited by 53,352
ENNRealstatement · cited by 9,879
Set.preimagestatement · cited by 4,946
PseudoEMetricSpacestatement · cited by 1,536
Metric.eballstatement · cited by 294
Isometrystatement · cited by 230
Isometry.preimage_eballproof · cited by 3

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