Theorems · Definition · functional analysis

LinearMap.IsContPerfPair.recOn

{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} →
                        {motive : p.IsContPerfPair → Sort u} →
                          (t : p.IsContPerfPair) →
                            ((continuous_uncurry :
                                  Continuous fun x =>
                                    match x with
                                    | (x, y) => (p x) y) →
                                (bijective_left : Function.Bijective fun x => { toLinearMap := p x, cont := ⋯ }) →
                                  (bijective_right :
                                      Function.Bijective fun y => { toLinearMap := p.flip y, cont := ⋯ }) →
                                    motive ⋯) →
                              motive t

Defined in

Mathlib.Topology.Algebra.Module.PerfectPairing

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace