Theorems · Theorem · general topology

Metric.tendstoUniformlyOnFilter_iff

∀ {α : Type u} {β : Type v} {ι : Type u_1} [inst : PseudoMetricSpace α] {F : ι → β → α} {f : β → α} {p : Filter ι}
  {p' : Filter β}, TendstoUniformlyOnFilter F f p p' ↔ ∀ ε > 0, ∀ᶠ (n : ι × β) in p ×ˢ p', dist (f n.2) (F n.1 n.2) < ε

Expressing uniform convergence using dist

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpace