Theorems · Theorem · general topology

AbstractCompletion.extend_unique

∀ {α : Type uα} [inst : UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [inst_1 : UniformSpace β]
  {f : α → β} [CompleteSpace β] [T0Space β],
  UniformContinuous f → ∀ {g : pkg.space → β}, UniformContinuous g → (∀ (a : α), f a = g (pkg.coe a)) → pkg.extend f = g

Defined in

Mathlib.Topology.UniformSpace.AbstractCompletion

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceCompleteSpaceT0Space