Theorems · Theorem · general topology

Metric.tendstoUniformlyOn_iff

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

Expressing uniform convergence on a set using dist.

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Basic

Cited by

14 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpace