Theorems · Definition · functional analysis

ContinuousAlternatingMap.toContinuousLinearMap

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_4} →
      {ι : Type u_6} →
        [inst : Semiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : TopologicalSpace M] →
                [inst_4 : AddCommMonoid N] →
                  [inst_5 : Module R N] →
                    [inst_6 : TopologicalSpace N] → M [⋀^ι]→L[R] N → [DecidableEq ι] → (ι → M) → ι → M →L[R] N

If f is a continuous alternating map, then f.toContinuousLinearMap m i is the continuous linear map obtained by fixing all coordinates but i equal to those of m, and varying the i-th coordinate.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

9 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceDecidableEq