Theorems · Theorem · general topology

Filter.Tendsto.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] {α : Type u_6} {l : Filter α} {f₁ f₂ : α → P}
  {g : α → R} {p₁ p₂ : P} {c : R},
  Filter.Tendsto f₁ l (nhds p₁) →
    Filter.Tendsto f₂ l (nhds p₂) →
      Filter.Tendsto g l (nhds c) →
        Filter.Tendsto (fun x => (AffineMap.lineMap (f₁ x) (f₂ x)) (g x)) l (nhds ((AffineMap.lineMap p₁ p₂) c))

Defined in

Mathlib.Topology.Algebra.Affine

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorRingModuleTopologicalSpaceContinuousSMul