Theorems · Theorem · global analysis
StructureGroupoid.subset_maximalAtlas
∀ {H : Type u} {M : Type u_2} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M] [inst_2 : ChartedSpace H M]
(G : StructureGroupoid H) [HasGroupoid M G], atlas H M ⊆ StructureGroupoid.maximalAtlas M GThe elements of the atlas belong to the maximal atlas for any structure groupoid.
- Defined in
- Mathlib.Geometry.Manifold.HasGroupoid
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ChartedSpacestatement and proof · cited by 2,397
- OpenPartialHomeomorphstatement and proof · cited by 664
- StructureGroupoidstatement and proof · cited by 121
- atlasstatement and proof · cited by 60
- StructureGroupoid.maximalAtlasstatement · cited by 28
- HasGroupoidstatement and proof · cited by 19
- StructureGroupoid.compatibleproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- IsManifold.subset_maximalAtlasproof · cited by 6
- StructureGroupoid.chart_mem_maximalAtlasproof · cited by 5
- StructureGroupoid.id_mem_maximalAtlasproof · cited by 2
- OpenPartialHomeomorph.mem_maximalAtlas_of_contMDiffOnproof · cited by 2
- StructureGroupoid.HasGroupoid.compproof · cited by 0