Theorems · Definition · functional analysis

NonUnitalSubalgebra.nonUnitalCommSemiringTopologicalClosure

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : TopologicalSpace A] →
        [inst_2 : NonUnitalSemiring A] →
          [inst_3 : Module R A] →
            [inst_4 : ContinuousConstSMul R A] →
              [inst_5 : IsSemitopologicalSemiring A] →
                [T2Space A] →
                  (s : NonUnitalSubalgebra R A) →
                    (∀ (x y : ↥s), x * y = y * x) → NonUnitalCommSemiring ↥s.topologicalClosure

If a non-unital subalgebra of a non-unital topological algebra is commutative, then so is its topological closure. See note [reducible non-instances].

Defined in

Mathlib.Topology.Algebra.NonUnitalAlgebra

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringTopologicalSpaceNonUnitalSemiringModuleContinuousConstSMulIsSemitopologicalSemiringT2Space