Theorems · Theorem · global analysis

UniqueMDiffWithinAt.bundle_preimage

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {F : Type u_9} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] {Z : M → Type u_10} [inst_8 : TopologicalSpace (Bundle.TotalSpace F Z)]
  [inst_9 : (b : M) → TopologicalSpace (Z b)] [inst_10 : FiberBundle F Z] {p : Bundle.TotalSpace F Z},
  UniqueMDiffAt[s] p.proj → UniqueMDiffAt[Bundle.TotalSpace.proj ⁻¹' s] p

In a fiber bundle, the preimage under the projection of a set with unique differentials in the base has unique differentials in the bundle.

Defined in

Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential

Cited by

2 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceFiberBundle