Theorems · Definition · functional analysis

ContinuousLinearMap.lcomp

{R : Type u_1} →
  {U : Type u_2} →
    {V : Type u_3} →
      (W : Type u_4) →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid U] →
            [inst_2 : Module R U] →
              [inst_3 : TopologicalSpace U] →
                [inst_4 : AddCommMonoid V] →
                  [inst_5 : Module R V] →
                    [inst_6 : TopologicalSpace V] →
                      [inst_7 : AddCommMonoid W] →
                        [inst_8 : Module R W] →
                          [inst_9 : TopologicalSpace W] →
                            [inst_10 : ContinuousAdd W] →
                              [inst_11 : ContinuousConstSMul R W] → (U →L[R] V) → (V →L[R] W) →ₗ[R] U →L[R] W

Composition of continuous linear maps, as a linear map. Compare LinearMap.lcomp.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMul