Theorems · Definition · general topology

EquicontinuousWithinAt

{ι : Type u_1} →
  {X : Type u_3} → {α : Type u_6} → [tX : TopologicalSpace X] → [uα : UniformSpace α] → (ι → X → α) → Set X → X → Prop

A family F : ι → X → α of functions from a topological space to a uniform space is equicontinuous at `x₀ : X` within `S : Set X` if, for all entourages U ∈ 𝓤 α, there is a neighborhood V of x₀ within S such that, for all x ∈ V and for all i : ι, F i x is U-close to F i x₀.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

24 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceUniformSpace