Theorems · Theorem · commutative algebra

UniformSpace.Completion.map_smul_eq_mul_coe

∀ (A : Type u_2) [inst : Ring A] [inst_1 : UniformSpace A] [IsUniformAddGroup A] [IsTopologicalRing A] (R : Type u_3)
  [inst_4 : CommSemiring R] [inst_5 : Algebra R A] [UniformContinuousConstSMul R A] (r : R),
  (UniformSpace.Completion.map fun x => r • x) = fun x => ↑((algebraMap R A) r) * x

Defined in

Mathlib.Topology.Algebra.UniformRing

Cited by

0 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingUniformSpaceIsUniformAddGroupIsTopologicalRingCommSemiringAlgebraUniformContinuousConstSMul