Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart

∀ {H : Type u_1} {M : Type u_2} {H' : Type u_3} {M' : Type u_4} [inst : TopologicalSpace H]
  [inst_1 : TopologicalSpace M] [inst_2 : ChartedSpace H M] [inst_3 : TopologicalSpace H']
  [inst_4 : TopologicalSpace M'] [inst_5 : ChartedSpace H' M'] {G : StructureGroupoid H} {G' : StructureGroupoid H'}
  {e : OpenPartialHomeomorph M H} {f : OpenPartialHomeomorph M' H'} {P : (H → H') → Set H → H → Prop} {g : M → M'}
  {s : Set M} {x : M},
  G.LocalInvariantProp G' P →
    e ∈ StructureGroupoid.maximalAtlas M G →
      x ∈ e.source →
        f ∈ StructureGroupoid.maximalAtlas M' G' →
          g x ∈ f.source →
            (ChartedSpace.LiftPropWithinAt P g s x ↔
              ContinuousWithinAt g s x ∧ P (↑f ∘ g ∘ ↑e.symm) (↑e.symm ⁻¹' s) (↑e x))

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

6 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceTopologicalSpaceChartedSpace