Theorems · Definition · global analysis

Diffeomorph.prodComm

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {F : Type u_4} →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] →
                {H : Type u_5} →
                  [inst_5 : TopologicalSpace H] →
                    {G : Type u_7} →
                      [inst_6 : TopologicalSpace G] →
                        (I : ModelWithCorners 𝕜 E H) →
                          (J : ModelWithCorners 𝕜 F G) →
                            (M : Type u_9) →
                              [inst_7 : TopologicalSpace M] →
                                [inst_8 : ChartedSpace H M] →
                                  (N : Type u_11) →
                                    [inst_9 : TopologicalSpace N] →
                                      [inst_10 : ChartedSpace G N] →
                                        (n : WithTop ℕ∞) → Diffeomorph (I.prod J) (J.prod I) (M × N) (N × M) n

M × N is diffeomorphic to N × M.

Defined in

Mathlib.Geometry.Manifold.Diffeomorph

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace