Theorems · Theorem · functional analysis

ContinuousAlgHom.coe_prodMap

∀ {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] {D : Type u_5}
  [inst_10 : Semiring D] [inst_11 : TopologicalSpace D] [inst_12 : Algebra R D] (f₁ : A →A[R] B) (f₂ : C →A[R] D),
  ↑(f₁.prodMap f₂) = (↑f₁).prodMap ↑f₂

Defined in

Mathlib.Topology.Algebra.Algebra

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebraSemiringAlgebraTopologicalSpaceSemiringTopologicalSpaceAlgebra