Theorems · Theorem · general topology

EquicontinuousAt.continuousAt

∀ {ι : Type u_1} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α] {F : ι → X → α} {x₀ : X},
  EquicontinuousAt F x₀ → ∀ (i : ι), ContinuousAt (F i) x₀

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

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