Theorems · Theorem · global analysis

extChartAt_mem_closure_interior

∀ {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]
  {I : ModelWithCorners 𝕜 E H} {s : Set M} [inst_5 : ChartedSpace H M] {x₀ x : M},
  x ∈ closure (interior s) →
    x ∈ (extChartAt I x₀).source →
      ↑(extChartAt I x₀) x ∈ closure (interior (↑(extChartAt I x₀).symm ⁻¹' s ∩ (extChartAt I x₀).target))

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

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace