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Theorems · Definition · convex and discrete geometry

ConvexCone.Pointed

{R : Type u_2} →
  {M : Type u_4} →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] → [inst_2 : AddCommMonoid M] → [inst_3 : SMul R M] → ConvexCone R M → Prop

A convex cone is pointed if it includes 0.

Defined in
Mathlib.Geometry.Convex.Cone.Basic
Cited by
14 results in Mathlib
Foundations
Depth 17 from the axioms · uses no axioms
Assumes
SemiringPartialOrderAddCommMonoidSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ConvexCone.toPointedCone · cited by 3ConvexCone.toPointedConePointedCone.pointed_toConvexCone · cited by 2PointedCone.pointed_toCon…ConvexCone.toPartialOrder · cited by 1ConvexCone.toPartialOrderConvexCone.blunt_iff_not_pointed · cited by 1ConvexCone.blunt_iff_not_…ConvexCone.Flat.pointed · cited by 1Flat.pointedConvexCone.coe_toPointedCone · cited by 0ConvexCone.coe_toPointedC…ConvexCone.Pointed.mono · cited by 0Pointed.monoConvexCone.Pointed.of_nonempty_of_isClosed · cited by 0Pointed.of_nonempty_of_is…ConvexCone.pointed_iff_not_blunt · cited by 0ConvexCone.pointed_iff_no…ConvexCone.toPreorder · cited by 0ConvexCone.toPreorderConvexCone.to_isOrderedAddMonoid · cited by 0ConvexCone.to_isOrderedAd…PointedCone.toConvexCone_closure_pointed · cited by 0PointedCone.toConvexCone_…ConvexCone.mem_toPointedCone · cited by 0ConvexCone.mem_toPointedC…ProperCone.pointed_toConvexCone · cited by 0ProperCone.pointed_toConv…Submodule.pointed_toConvexCone · cited by 0Submodule.pointed_toConve…Semiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderConvexCone · cited by 103ConvexConeConvexCone.PointedCITED BYCITES

Cites4

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

Cited by17

Results whose statement or proof uses this declaration.