Theorems · Definition · functional analysis

NonUnitalStarSubalgebra.topologicalClosure

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : TopologicalSpace A] →
        [inst_2 : Star A] →
          [inst_3 : NonUnitalSemiring A] →
            [inst_4 : Module R A] →
              [ContinuousStar A] →
                [ContinuousConstSMul R A] →
                  [IsSemitopologicalSemiring A] → NonUnitalStarSubalgebra R A → NonUnitalStarSubalgebra R A

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

Defined in

Mathlib.Topology.Algebra.NonUnitalStarAlgebra

Cited by

12 results in Mathlib

Foundations

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

Assumes

CommSemiringTopologicalSpaceStarNonUnitalSemiringModuleContinuousStarContinuousConstSMulIsSemitopologicalSemiring