Theorems · Theorem · general topology

Filter.Tendsto.midpoint

∀ {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}
  [inst_9 : Invertible 2] {f₁ f₂ : α → P} {p₁ p₂ : P},
  Filter.Tendsto f₁ l (nhds p₁) →
    Filter.Tendsto f₂ l (nhds p₂) → Filter.Tendsto (fun x => midpoint R (f₁ x) (f₂ x)) l (nhds (midpoint R p₁ p₂))

Defined in

Mathlib.Topology.Algebra.Affine

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorRingModuleTopologicalSpaceContinuousSMulInvertible