Theorems · Theorem · general topology

ContinuousMap.compStarAlgHom_apply

∀ (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) (hφ : Continuous ⇑φ) (f : C(X, A)),
  (ContinuousMap.compStarAlgHom X φ hφ) f = { toFun := ⇑φ, continuous_toFun := hφ }.comp f

Defined in

Mathlib.Topology.ContinuousMap.Star

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommSemiringTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebraTopologicalSpaceSemiringIsTopologicalSemiringStarContinuousStarAlgebra