Theorems · Definition · global analysis

Manifold.LiftSourceTargetPropertyAt.domChart

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_4} →
      {H : Type u_6} →
        {G : Type u_8} →
          [inst : NontriviallyNormedField 𝕜] →
            [inst_1 : NormedAddCommGroup E] →
              [inst_2 : NormedSpace 𝕜 E] →
                [inst_3 : NormedAddCommGroup F] →
                  [inst_4 : NormedSpace 𝕜 F] →
                    [inst_5 : TopologicalSpace H] →
                      [inst_6 : TopologicalSpace G] →
                        {I : ModelWithCorners 𝕜 E H} →
                          {J : ModelWithCorners 𝕜 F G} →
                            {M : Type u_10} →
                              {N : Type u_12} →
                                [inst_7 : TopologicalSpace M] →
                                  [inst_8 : ChartedSpace H M] →
                                    [inst_9 : TopologicalSpace N] →
                                      [inst_10 : ChartedSpace G N] →
                                        {n : WithTop ℕ∞} →
                                          {f : M → N} →
                                            {x : M} →
                                              {P :
                                                  (M → N) →
                                                    OpenPartialHomeomorph M H → OpenPartialHomeomorph N G → Prop} →
                                                Manifold.LiftSourceTargetPropertyAt I J n f x P →
                                                  OpenPartialHomeomorph M H

A choice of chart on the domain M of a local property of f at x: w.r.t. this chart and h.codChart, f has the local property P at x. The particular chart is arbitrary, but this choice matches the witness given by h.codChart.

Defined in

Mathlib.Geometry.Manifold.LocalSourceTargetProperty

Cited by

8 results in Mathlib

Foundations

Depth 15 from the axioms · uses Classical.choice

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace