Theorems · Definition · functional analysis

LineDeriv.lineDerivOpCLM

(R : Type u_4) →
  {V : Type u_5} →
    (E : Type u_6) →
      {F : Type u_7} →
        [inst : Ring R] →
          [inst_1 : AddCommGroup E] →
            [inst_2 : Module R E] →
              [inst_3 : AddCommGroup F] →
                [inst_4 : Module R F] →
                  [inst_5 : TopologicalSpace E] →
                    [inst_6 : TopologicalSpace F] →
                      [inst_7 : AddCommGroup V] →
                        [inst_8 : LineDeriv V E F] →
                          [LineDerivAdd V E F] → [LineDerivSMul R V E F] → [ContinuousLineDeriv V E F] → V → E →L[R] F

The line derivative as a continuous linear map.

Defined in

Mathlib.Analysis.Distribution.DerivNotation

Cited by

9 results in Mathlib

Foundations

Depth 17 from the axioms · uses no axioms

Assumes

RingAddCommGroupModuleAddCommGroupModuleTopologicalSpaceTopologicalSpaceAddCommGroupLineDerivLineDerivAddLineDerivSMulContinuousLineDeriv