Theorems · Theorem · functional analysis

ContinuousAlgHom.prod_apply

∀ {R : Type u_1} [inst : CommSemiring R] {A : Type u_2} [inst_1 : Semiring A] [inst_2 : TopologicalSpace A]
  {B : Type u_3} [inst_3 : Semiring B] [inst_4 : TopologicalSpace B] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  {C : Type u_4} [inst_7 : Semiring C] [inst_8 : Algebra R C] [inst_9 : TopologicalSpace C] (f₁ : A →A[R] B)
  (f₂ : A →A[R] C) (x : A), (f₁.prod f₂) x = (f₁ x, f₂ x)

Defined in

Mathlib.Topology.Algebra.Algebra

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebraSemiringAlgebraTopologicalSpace