Theorems · Definition · general topology

ContinuousMap.unitsOfForallIsUnit

{X : Type u_1} →
  {R : Type u_3} →
    [inst : TopologicalSpace X] →
      [inst_1 : NormedRing R] → [CompleteSpace R] → {f : C(X, R)} → (∀ (x : X), IsUnit (f x)) → C(X, Rˣ)

Construct a continuous map into the group of units of a normed ring from a function into the normed ring and a proof that every element of the range is a unit.

Defined in

Mathlib.Topology.ContinuousMap.Units

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNormedRingCompleteSpace