Theorems · Theorem · general topology

EquicontinuousOn.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}, EquicontinuousOn F S → ∀ (u : κ → ι), EquicontinuousOn (F ∘ u) S

Taking sub-families preserves equicontinuity on a subset.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceUniformSpace