Theorems · Definition · algebraic geometry

ChartedSpace.locallyRingedSpaceMapAux

{𝕜 : Type u} →
  [inst : NontriviallyNormedField 𝕜] →
    {EM : Type u_1} →
      [inst_1 : NormedAddCommGroup EM] →
        [inst_2 : NormedSpace 𝕜 EM] →
          {HM : Type u_2} →
            [inst_3 : TopologicalSpace HM] →
              {IM : ModelWithCorners 𝕜 EM HM} →
                {M : Type u} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace HM M] →
                      {EN : Type u_3} →
                        [inst_6 : NormedAddCommGroup EN] →
                          [inst_7 : NormedSpace 𝕜 EN] →
                            {HN : Type u_4} →
                              [inst_8 : TopologicalSpace HN] →
                                {IN : ModelWithCorners 𝕜 EN HN} →
                                  {N : Type u} →
                                    [inst_9 : TopologicalSpace N] →
                                      [inst_10 : ChartedSpace HN N] →
                                        (f : M → N) →
                                          ContMDiff IM IN (↑⊤) f →
                                            ((ChartedSpace.locallyRingedSpace IM M).toPresheafedSpace ⟶
                                              (ChartedSpace.locallyRingedSpace IN N).toPresheafedSpace)

(Implementation): Use ChartedSpace.locallyRingedSpaceMap.

Defined in

Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace

Cited by

1 results in Mathlib

Foundations

Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace