Theorems · Definition · functional analysis

ContinuousLinearMap.llcomp

(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 : ContinuousAdd V] →
                        [inst_8 : ContinuousConstSMul R V] →
                          [inst_9 : AddCommMonoid W] →
                            [inst_10 : Module R W] →
                              [inst_11 : TopologicalSpace W] →
                                [inst_12 : ContinuousAdd W] →
                                  [inst_13 : ContinuousConstSMul R W] → (U →L[R] V) →ₗ[R] (V →L[R] W) →ₗ[R] U →L[R] W

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

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMul