Theorems · Theorem · general topology

Filter.Tendsto.inseparable_iff_uniformity

∀ {α : Type u} [inst : UniformSpace α] {β : Type u_1} {l : Filter β} [l.NeBot] {f g : β → α} {a b : α},
  Filter.Tendsto f l (nhds a) →
    Filter.Tendsto g l (nhds b) → (Inseparable a b ↔ Filter.Tendsto (fun x => (f x, g x)) l (uniformity α))

Defined in

Mathlib.Topology.UniformSpace.Separation

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceFilter.NeBot