Theorems · Theorem · general topology

equicontinuousAt_iff_pair

∀ {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 ↔ ∀ U ∈ uniformity α, ∃ V ∈ nhds x₀, ∀ x ∈ V, ∀ y ∈ V, ∀ (i : ι), (F i x, F i y) ∈ U

Reformulation of equicontinuity at x₀ comparing two variables near x₀ instead of comparing only one with x₀.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace