Theorems · Theorem · general topology

ContinuousMap.continuous_isUnit_unit

∀ {X : Type u_1} {R : Type u_3} [inst : TopologicalSpace X] [inst_1 : NormedRing R] [CompleteSpace R] {f : C(X, R)}
  (h : ∀ (x : X), IsUnit (f x)), Continuous fun x => ⋯.unit

Defined in

Mathlib.Topology.ContinuousMap.Units

Cited by

0 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNormedRingCompleteSpace