Theorems · Theorem · general topology

EquicontinuousWithinAt.continuousWithinAt

∀ {ι : Type u_1} {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 → ∀ (i : ι), ContinuousWithinAt (F i) S x₀

Each function of a family equicontinuous at x₀ within S is continuous at x₀ within S.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

2 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace