Theorems · Theorem · Lie groups

TendstoLocallyUniformlyOn.fun_mul

∀ {α : Type u_1} [inst : UniformSpace α] [inst_1 : Group α] [IsUniformGroup α] {ι : Type u_3} {X : Type u_4}
  [inst_3 : TopologicalSpace X] {F G : ι → X → α} {f g : X → α} {s : Set X} {l : Filter ι},
  TendstoLocallyUniformlyOn F f l s →
    TendstoLocallyUniformlyOn G g l s →
      TendstoLocallyUniformlyOn (fun i i_1 => F i i_1 * G i i_1) (fun i => f i * g i) l s

Eta-expanded form of TendstoLocallyUniformlyOn.mul

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceGroupIsUniformGroupTopologicalSpace