Theorems · Definition · functional analysis

LinearMap.toContPerfPair

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : TopologicalSpace R] →
          [inst_2 : AddCommGroup M] →
            [inst_3 : Module R M] →
              [inst_4 : TopologicalSpace M] →
                [inst_5 : AddCommGroup N] →
                  [inst_6 : Module R N] →
                    [inst_7 : TopologicalSpace N] →
                      (p : M →ₗ[R] N →ₗ[R] R) →
                        [p.IsContPerfPair] → [inst_9 : IsTopologicalRing R] → M ≃ₗ[R] StrongDual R N

Turn a continuous perfect pairing between M and N into a map from M to continuous linear maps N → R.

Defined in

Mathlib.Topology.Algebra.Module.PerfectPairing

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceLinearMap.IsContPerfPairIsTopologicalRing