Theorems · Theorem · general topology

Metric.equicontinuousAt_iff_right

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] {ι : Type u_4} [inst_1 : TopologicalSpace β]
  {F : ι → β → α} {x₀ : β}, EquicontinuousAt F x₀ ↔ ∀ ε > 0, ∀ᶠ (x : β) in nhds x₀, ∀ (i : ι), dist (F i x₀) (F i x) < ε

Characterization of equicontinuity for families of functions taking values in a (pseudo) metric space.

Defined in

Mathlib.Topology.MetricSpace.Equicontinuity

Cited by

2 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceTopologicalSpace