Theorems · Definition · convex and discrete geometry

Geometry.SimplicialComplex.space

{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 underlying space of a simplicial complex is the union of its faces.

Defined in: Mathlib.Analysis.Convex.SimplicialComplex.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring PartialOrder AddCommGroup Module

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
Finsetproof · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
SetLike.coeproof · cited by 8,199
Ringstatement and proof · cited by 7,463
PartialOrderstatement and proof · cited by 6,410
Set.iUnionproof · cited by 2,483
convexHullproof · cited by 163
PreAbstractSimplicialComplex.facesproof · cited by 36
Geometry.SimplicialComplexstatement and proof · cited by 27

Cited by5

Results whose statement or proof uses this declaration.

Geometry.SimplicialComplex.convexHull_subset_spacestatement and proof · cited by 1
Geometry.SimplicialComplex.mem_space_iffstatement · cited by 0
Geometry.SimplicialComplex.space_botstatement · cited by 0
Geometry.SimplicialComplex.subset_spacestatement · cited by 0
Geometry.SimplicialComplex.vertices_subset_spacestatement · cited by 0