Theorems · Definition · functional analysis

ContinuousLinearMap.coeLM

{R : Type u_1} →
  (S : Type u_4) →
    [inst : Semiring R] →
      [inst_1 : Semiring S] →
        {M : Type u_6} →
          [inst_2 : TopologicalSpace M] →
            [inst_3 : AddCommMonoid M] →
              [inst_4 : Module R M] →
                {N₃ : Type u_10} →
                  [inst_5 : TopologicalSpace N₃] →
                    [inst_6 : AddCommMonoid N₃] →
                      [inst_7 : Module R N₃] →
                        [inst_8 : Module S N₃] →
                          [inst_9 : SMulCommClass R S N₃] →
                            [inst_10 : ContinuousConstSMul S N₃] →
                              [inst_11 : ContinuousAdd N₃] → (M →L[R] N₃) →ₗ[S] M →ₗ[R] N₃

The coercion from M →L[R] M₂ to M →ₗ[R] M₂, as a linear map.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

5 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleModuleSMulCommClassContinuousConstSMulContinuousAdd