Theorems · Theorem · general topology

ContinuousAt.lineMap

∀ {R : Type u_1} {V : Type u_2} {P : Type u_3} [inst : AddCommGroup V] [inst_1 : TopologicalSpace V]
  [inst_2 : AddTorsor V P] [inst_3 : TopologicalSpace P] [IsTopologicalAddTorsor P] [inst_5 : Ring R]
  [inst_6 : Module R V] [inst_7 : TopologicalSpace R] [ContinuousSMul R V] {X : Type u_6} [inst_9 : TopologicalSpace X]
  {f₁ f₂ : X → P} {g : X → R} {x : X},
  ContinuousAt f₁ x →
    ContinuousAt f₂ x → ContinuousAt g x → ContinuousAt (fun x => (AffineMap.lineMap (f₁ x) (f₂ x)) (g x)) x

Defined in

Mathlib.Topology.Algebra.Affine

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorRingModuleTopologicalSpaceContinuousSMulTopologicalSpace