Theorems · Theorem · global analysis

UniqueMDiffOn.tangentBundle_proj_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] [inst_6 : IsManifold I 1 M] {s : Set M},
  UniqueMDiff[s] → UniqueMDiff[Bundle.TotalSpace.proj ⁻¹' s]

The preimage under the projection from the tangent bundle of a set with unique differential in the basis also has unique differential.

Defined in

Mathlib.Geometry.Manifold.MFDeriv.Tangent

Cited by

0 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold