Theorems · Theorem · general topology

TendstoLocallyUniformly.congr_inseparable

∀ {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} {p : Filter ι} {G : ι → α → β},
  TendstoLocallyUniformly F f p →
    (∀ᶠ (n : ι) in p, ∀ (x : α), Inseparable (F n x) (G n x)) → TendstoLocallyUniformly G f p

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace