Theorems · Definition · combinatorics
PreAbstractSimplicialComplex.faces
{ι : Type u_1} → PreAbstractSimplicialComplex ι → Set (Finset ι)the faces of this simplicial complex: currently, given by their spanning vertices
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- PreAbstractSimplicialComplexstatement and proof · cited by 16
Cited by54
Results whose statement or proof uses this declaration.
- Geometry.SimplicialComplex.spaceproof · cited by 5
- Geometry.SimplicialComplex.facetsproof · cited by 4
- Geometry.SimplicialComplex.verticesproof · cited by 4
- Geometry.SimplicialComplex.down_closedstatement and proof · cited by 3
- Geometry.SimplicialComplex.inter_subset_convexHullstatement · cited by 3
- AbstractSimplicialComplex.extstatement and proof · cited by 2
- PreAbstractSimplicialComplex.isRelLowerSet_facesstatement · cited by 2
- Geometry.SimplicialComplex.convexHull_inter_convexHullstatement and proof · cited by 1
- Geometry.SimplicialComplex.convexHull_subset_spacestatement and proof · cited by 1
- Geometry.SimplicialComplex.extstatement and proof · cited by 1
- Geometry.SimplicialComplex.facets_subsetstatement · cited by 1
- Geometry.SimplicialComplex.mk.injstatement and proof · cited by 1