Theorems · Definition · general topology

TendstoUniformlyOnFilter

{α : Type u_1} → {β : Type u_2} → {ι : Type u_4} → [UniformSpace β] → (ι → α → β) → (α → β) → Filter ι → Filter α → Prop

A sequence of functions Fₙ converges uniformly on a filter p' to a limiting function f with respect to the filter p if, for any entourage of the diagonal u, one has p ×ˢ p'-eventually (f x, Fₙ x) ∈ u.

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

50 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace