Theorems · Theorem · general topology

Metric.tendstoUniformly_iff

∀ {α : Type u} {β : Type v} {ι : Type u_1} [inst : PseudoMetricSpace α] {F : ι → β → α} {f : β → α} {p : Filter ι},
  TendstoUniformly F f p ↔ ∀ ε > 0, ∀ᶠ (n : ι) in p, ∀ (x : β), dist (f x) (F n x) < ε

Expressing uniform convergence using dist.

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Basic

Cited by

1 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace