Theorems · Definition · functional analysis

ContinuousMultilinearMap.toUniformOnFun

{𝕜 : Type u_1} →
  {ι : Type u_2} →
    {E : ι → Type u_3} →
      {F : Type u_4} →
        [inst : NormedField 𝕜] →
          [inst_1 : (i : ι) → TopologicalSpace (E i)] →
            [inst_2 : (i : ι) → AddCommGroup (E i)] →
              [inst_3 : (i : ι) → Module 𝕜 (E i)] →
                [inst_4 : AddCommGroup F] →
                  [inst_5 : Module 𝕜 F] →
                    [inst_6 : TopologicalSpace F] →
                      ContinuousMultilinearMap 𝕜 E F → UniformOnFun ((i : ι) → E i) F {s | Bornology.IsVonNBounded 𝕜 s}

An auxiliary definition used to define topology on ContinuousMultilinearMap 𝕜 E F.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

7 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleAddCommGroupModuleTopologicalSpace