Theorems · Theorem · general topology

Isometry.isCover_image_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {ε : NNReal} {s : Set X}
  {f : X → Y}, Isometry f → ∀ (C : Set X), Metric.IsCover ε (f '' s) (f '' C) ↔ Metric.IsCover ε s C

Defined in

Mathlib.Topology.MetricSpace.Cover

Cited by

1 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace