Theorems · Definition · functional analysis

ContinuousAlgHom.casesOn

{R : Type u_3} →
  [inst : CommSemiring R] →
    {A : Type u_4} →
      [inst_1 : Semiring A] →
        [inst_2 : TopologicalSpace A] →
          {B : Type u_5} →
            [inst_3 : Semiring B] →
              [inst_4 : TopologicalSpace B] →
                [inst_5 : Algebra R A] →
                  [inst_6 : Algebra R B] →
                    {motive : (A →A[R] B) → Sort u} →
                      (t : A →A[R] B) →
                        ((toAlgHom : A →ₐ[R] B) →
                            (cont : Continuous (↑↑toAlgHom.toRingHom).toFun) →
                              motive { toAlgHom := toAlgHom, cont := cont }) →
                          motive t

Defined in

Mathlib.Topology.Algebra.Algebra

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

CommSemiringSemiringTopologicalSpaceSemiringTopologicalSpaceAlgebraAlgebra