Theorems · Definition · general topology

ContinuousMap.compStarAlgHom

(X : Type u_1) →
  {𝕜 : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        [inst : TopologicalSpace X] →
          [inst_1 : CommSemiring 𝕜] →
            [inst_2 : TopologicalSpace A] →
              [inst_3 : Semiring A] →
                [inst_4 : IsTopologicalSemiring A] →
                  [inst_5 : Star A] →
                    [inst_6 : ContinuousStar A] →
                      [inst_7 : Algebra 𝕜 A] →
                        [inst_8 : TopologicalSpace B] →
                          [inst_9 : Semiring B] →
                            [inst_10 : IsTopologicalSemiring B] →
                              [inst_11 : Star B] →
                                [inst_12 : ContinuousStar B] →
                                  [inst_13 : Algebra 𝕜 B] → (φ : A →⋆ₐ[𝕜] B) → Continuous ⇑φ → C(X, A) →⋆ₐ[𝕜] C(X, B)

Post-composition with a continuous star algebra homomorphism is a star algebra homomorphism between spaces of continuous maps.

Defined in

Mathlib.Topology.ContinuousMap.Star

Cited by

4 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommSemiringTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebraTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebra