Theorems · Theorem · general topology

tendstoLocallyUniformlyOn_biUnion

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β]
  {F : ι → α → β} {f : α → β} {p : Filter ι} {s : Set γ} {S : γ → Set α},
  (∀ i ∈ s, IsOpen (S i)) →
    (∀ i ∈ s, TendstoLocallyUniformlyOn F f p (S i)) → TendstoLocallyUniformlyOn F f p (⋃ i ∈ s, S i)

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace