Theorems · Theorem · global analysis

Manifold.IsLocalSourceTargetProperty.mono_source

∀ {H : Type u_6} {G : Type u_8} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace G] {M : Type u_10}
  {N : Type u_12} [inst_2 : TopologicalSpace M] [inst_3 : TopologicalSpace N]
  {P : (M → N) → OpenPartialHomeomorph M H → OpenPartialHomeomorph N G → Prop},
  Manifold.IsLocalSourceTargetProperty P →
    ∀ {f : M → N} {φ : OpenPartialHomeomorph M H} {ψ : OpenPartialHomeomorph N G} {s : Set M},
      IsOpen s → P f φ ψ → P f (φ.restr s) ψ

Defined in

Mathlib.Geometry.Manifold.LocalSourceTargetProperty

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace