Theorems · Theorem · manifolds

ChartedSpace.mem_atlas_sum

∀ {H : Type u} {M : Type u_2} {M' : Type u_3} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace M'] [cm : ChartedSpace H M] [cm' : ChartedSpace H M'] [h : Nonempty H]
  {e : OpenPartialHomeomorph (M ⊕ M') H},
  e ∈ atlas H (M ⊕ M') → (∃ f ∈ atlas H M, e = f.lift_openEmbedding ⋯) ∨ ∃ f' ∈ atlas H M', e = f'.lift_openEmbedding ⋯

Defined in

Mathlib.Geometry.Manifold.ChartedSpace

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceChartedSpaceNonempty