Theorems · Theorem · global analysis

StructureGroupoid.LocalInvariantProp.is_local_nhds

∀ {H : Type u_1} {H' : Type u_3} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace H'] {G : StructureGroupoid H}
  {G' : StructureGroupoid H'} {P : (H → H') → Set H → H → Prop},
  G.LocalInvariantProp G' P → ∀ {s u : Set H} {x : H} {f : H → H'}, u ∈ nhdsWithin x s → (P f s x ↔ P f (s ∩ u) x)

Defined in

Mathlib.Geometry.Manifold.LocalInvariantProperties

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace