Theorems · Theorem · geometry

ContinuousAt.inversion

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {X : Type u_3} [inst_4 : TopologicalSpace X] {c x : X → P} {R : X → ℝ} {a₀ : X},
  ContinuousAt c a₀ →
    ContinuousAt R a₀ →
      ContinuousAt x a₀ → x a₀ ≠ c a₀ → ContinuousAt (fun a => EuclideanGeometry.inversion (c a) (R a) (x a)) a₀

Defined in

Mathlib.Geometry.Euclidean.Inversion.Basic

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorTopologicalSpace