Theorems · Definition · functional analysis

NonUnitalSubalgebra.topologicalClosure

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : TopologicalSpace A] →
        [inst_2 : NonUnitalSemiring A] →
          [inst_3 : Module R A] →
            [ContinuousConstSMul R A] →
              [IsSemitopologicalSemiring A] → NonUnitalSubalgebra R A → NonUnitalSubalgebra R A

The (topological) closure of a non-unital subalgebra of a non-unital topological algebra is itself a non-unital subalgebra.

Defined in

Mathlib.Topology.Algebra.NonUnitalAlgebra

Cited by

8 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceNonUnitalSemiringModuleContinuousConstSMulIsSemitopologicalSemiring