Theorems · Theorem · general topology

Filter.HasBasis.uniformEquicontinuous_iff_left

∀ {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 (β × β)} {F : ι → β → α},
  (uniformity β).HasBasis p s →
    (UniformEquicontinuous F ↔ ∀ U ∈ uniformity α, ∃ k, p k ∧ ∀ (x y : β), (x, y) ∈ s k → ∀ (i : ι), (F i x, F i y) ∈ U)

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

0 results in Mathlib

Foundations

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

Assumes

UniformSpaceUniformSpace