Theorems · Theorem · general topology

IsometryEquiv.preimage_sphere

∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] (h : α ≃ᵢ β) (x : β) (r : ℝ),
  ⇑h ⁻¹' Metric.sphere x r = Metric.sphere (h.symm x) r

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

4 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpace