Theorems · Definition · convex and discrete geometry

Geometry.SimplicialComplex.vertices

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : Ring 𝕜] →
      [inst_1 : PartialOrder 𝕜] →
        [inst_2 : AddCommGroup E] → [inst_3 : Module 𝕜 E] → Geometry.SimplicialComplex 𝕜 E → Set E

The vertices of a simplicial complex are its zero-dimensional faces.

Defined in: Mathlib.Analysis.Convex.SimplicialComplex.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Quot.sound
Assumes: Ring PartialOrder AddCommGroup Module

Mathlib docs Source Loogle LeanSearch

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
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
PartialOrderstatement and proof · cited by 6,410
Set.ofPredproof · cited by 6,101
PreAbstractSimplicialComplex.facesproof · cited by 36
Geometry.SimplicialComplexstatement and proof · cited by 27
Geometry.SimplicialComplex.toPreAbstractSimplicialComplexproof · cited by 23

Cited by4

Results whose statement or proof uses this declaration.

Geometry.SimplicialComplex.vertex_mem_convexHull_iffstatement and proof · cited by 1
Geometry.SimplicialComplex.vertices_eqstatement and proof · cited by 1
Geometry.SimplicialComplex.mem_verticesstatement · cited by 0
Geometry.SimplicialComplex.vertices_subset_spacestatement · cited by 0