Theorems · Definition · general topology

TendstoUniformly

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

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

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

75 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

UniformSpace