Theorems · Theorem · global analysis

OpenPartialHomeomorph.mem_interior_extend_target

∀ {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 : OpenPartialHomeomorph M H) {I : ModelWithCorners 𝕜 E H} {y : H},
  y ∈ f.target → ↑I y ∈ interior (Set.range ↑I) → ↑I y ∈ interior (f.extend I).target

If y ∈ f.target and I y ∈ interior (range I), then I y is an interior point of (I ∘ f).target.

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

2 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace