Theorems · Theorem · global analysis

Manifold.IsImmersionAt.isImmersionAtOfComplement_complement

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {E'' : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup E''] [inst_4 : NormedSpace 𝕜 E''] {H : Type u_7}
  [inst_5 : TopologicalSpace H] {G : Type u_9} [inst_6 : TopologicalSpace G] {I : ModelWithCorners 𝕜 E H}
  {J : ModelWithCorners 𝕜 E'' G} {M : Type u_11} [inst_7 : TopologicalSpace M] [inst_8 : ChartedSpace H M]
  {N : Type u_13} [inst_9 : TopologicalSpace N] [inst_10 : ChartedSpace G N] {n : WithTop ℕ∞} {f : M → N} {x : M}
  (h : Manifold.IsImmersionAt I J n f x), Manifold.IsImmersionAtOfComplement h.complement I J n f x

Defined in

Mathlib.Geometry.Manifold.Immersion

Cited by

16 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace