Theorems · Theorem · general topology

EquicontinuousWithinAt.comp

∀ {ι : Type u_1} {κ : Type u_2} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α]
  {F : ι → X → α} {S : Set X} {x₀ : X},
  EquicontinuousWithinAt F S x₀ → ∀ (u : κ → ι), EquicontinuousWithinAt (F ∘ u) S x₀

Taking sub-families preserves equicontinuity at a point within a subset.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

2 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceUniformSpace