Theorems · Definition · functional analysis

ContinuousAlgHom.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] → (A →A[R] B) → (C →A[R] D) → A × C →A[R] B × D

Prod.map of two continuous algebra homomorphisms.

Defined in

Mathlib.Topology.Algebra.Algebra

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebraSemiringAlgebraTopologicalSpaceSemiringTopologicalSpaceAlgebra