Theorems · Theorem · general topology

Metric.equicontinuousAt_iff_pair

∀ {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, ∃ U ∈ nhds x₀, ∀ x ∈ U, ∀ x' ∈ U, ∀ (i : ι), dist (F i x) (F i x') < ε

Reformulation of equicontinuousAt_iff_pair for families of functions taking values in a (pseudo) metric space.

Defined in

Mathlib.Topology.MetricSpace.Equicontinuity

Cited by

0 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceTopologicalSpace