Theorems · Theorem · general topology

TendstoLocallyUniformlyOn.union

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {F : ι → α → β}
  {f : α → β} {s s' : Set α} {p : Filter ι},
  IsOpen s →
    IsOpen s' →
      TendstoLocallyUniformlyOn F f p s → TendstoLocallyUniformlyOn F f p s' → TendstoLocallyUniformlyOn F f p (s ∪ s')

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace