Theorems · Theorem · general topology

Equicontinuous.continuous

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

Each function of an equicontinuous family is continuous.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

3 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace