Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target

∀ {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'}
  {f : OpenPartialHomeomorph M' H'} {P : (H → H') → Set H → H → Prop} {g : M → M'} {s : Set M} {x : M},
  G.LocalInvariantProp G' P →
    f ∈ StructureGroupoid.maximalAtlas M' G' →
      g x ∈ f.source →
        (ChartedSpace.LiftPropWithinAt P g s x ↔
          ContinuousWithinAt g s x ∧ ChartedSpace.LiftPropWithinAt P (↑f ∘ g) s x)

A version of liftPropWithinAt_indep_chart, only for the target.

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceTopologicalSpaceChartedSpace