Theorems · Theorem · global analysis

OpenPartialHomeomorph.extend_prod

∀ {𝕜 : Type u_1} {E : Type u_2} {M : Type u_3} {H : Type u_4} {E' : Type u_5} {M' : Type u_6} {H' : Type u_7}
  [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
  [inst_3 : TopologicalSpace H] [inst_4 : TopologicalSpace M] (f : OpenPartialHomeomorph M H)
  {I : ModelWithCorners 𝕜 E H} [inst_5 : NormedAddCommGroup E'] [inst_6 : NormedSpace 𝕜 E']
  [inst_7 : TopologicalSpace H'] [inst_8 : TopologicalSpace M'] {I' : ModelWithCorners 𝕜 E' H'}
  (f' : OpenPartialHomeomorph M' H'), (f.prod f').extend (I.prod I') = (f.extend I).prod (f'.extend I')

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

2 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace