Theorems · Definition · general topology

CauchyFilter.extend

{α : Type u} → [inst : UniformSpace α] → {β : Type v} → [UniformSpace β] → (α → β) → CauchyFilter α → β

Extend a uniformly continuous function α → β to a function CauchyFilter α → β. Outputs junk when f is not uniformly continuous.

Defined in

Mathlib.Topology.UniformSpace.Completion

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace