Theorems · Theorem · general topology

Filter.HasBasis.equicontinuousWithinAt_iff_left

∀ {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 X} {F : ι → X → α} {S : Set X} {x₀ : X},
  (nhdsWithin x₀ S).HasBasis p s →
    (EquicontinuousWithinAt F S x₀ ↔ ∀ U ∈ uniformity α, ∃ k, p k ∧ ∀ x ∈ s k, ∀ (i : ι), (F i x₀, F i x) ∈ U)

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceUniformSpace