Theorems · Theorem · general topology

Metric.tendstoLocallyUniformlyOn_iff

∀ {α : Type u} {β : Type v} {ι : Type u_1} [inst : PseudoMetricSpace α] [inst_1 : TopologicalSpace β] {F : ι → β → α}
  {f : β → α} {p : Filter ι} {s : Set β},
  TendstoLocallyUniformlyOn F f p s ↔
    ∀ ε > 0, ∀ x ∈ s, ∃ t ∈ nhdsWithin x s, ∀ᶠ (n : ι) in p, ∀ y ∈ t, dist (f y) (F n y) < ε

Expressing locally uniform convergence on a set using dist.

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpaceTopologicalSpace