Theorems · Theorem · general topology

Filter.HasBasis.uniformEquicontinuous_iff_right

∀ {ι : Type u_1} {κ : Type u_2} {α : Type u_6} {β : Type u_8} [uα : UniformSpace α] [uβ : UniformSpace β] {p : κ → Prop}
  {s : κ → Set (α × α)} {F : ι → β → α},
  (uniformity α).HasBasis p s →
    (UniformEquicontinuous F ↔ ∀ (k : κ), p k → ∀ᶠ (xy : β × β) in uniformity β, ∀ (i : ι), (F i xy.1, F i xy.2) ∈ s k)

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace