Theorems · Theorem · general topology

Filter.HasBasis.equicontinuousAt_iff_right

∀ {ι : Type u_1} {κ : Type u_2} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α]
  {p : κ → Prop} {s : κ → Set (α × α)} {F : ι → X → α} {x₀ : X},
  (uniformity α).HasBasis p s →
    (EquicontinuousAt F x₀ ↔ ∀ (k : κ), p k → ∀ᶠ (x : X) in nhds x₀, ∀ (i : ι), (F i x₀, F i x) ∈ s k)

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

3 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace