Theorems · Definition · global analysis

ModelWithCorners.prod

{𝕜 : Type u} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type v} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type w} →
            [inst_3 : TopologicalSpace H] →
              ModelWithCorners 𝕜 E H →
                {E' : Type v'} →
                  [inst_4 : NormedAddCommGroup E'] →
                    [inst_5 : NormedSpace 𝕜 E'] →
                      {H' : Type w'} →
                        [inst_6 : TopologicalSpace H'] →
                          ModelWithCorners 𝕜 E' H' → ModelWithCorners 𝕜 (E × E') (ModelProd H H')

Given two model_with_corners I on (E, H) and I' on (E', H'), we define the model with corners I.prod I' on (E × E', ModelProd H H'). This appears in particular for the manifold structure on the tangent bundle to a manifold modelled on (E, H): it will be modelled on (E × E, H × E). See note [Manifold type tags] for explanation about ModelProd H H' vs H × H'.

Defined in

Mathlib.Geometry.Manifold.IsManifold.Basic

Cited by

414 results in Mathlib

Foundations

Depth 166 from the axioms, rests on 4,067 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpace