Theorems · Theorem · global analysis

OpenPartialHomeomorph.extend_image_source_inter

∀ {𝕜 : Type u_1} {E : Type u_2} {M : Type u_3} {H : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] [inst_4 : TopologicalSpace M]
  (f f' : OpenPartialHomeomorph M H) {I : ModelWithCorners 𝕜 E H},
  ↑(f.extend I) '' (f.source ∩ f'.source) = (ModelWithCorners.extendCoordChange f f').source

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

3 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace