Theorems · Definition · convex and discrete geometry

ProperCone.positive

(R : Type u_2) →
  (E : Type u_3) →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] →
        [inst_2 : IsOrderedRing R] →
          [inst_3 : AddCommMonoid E] →
            [inst_4 : TopologicalSpace E] →
              [inst_5 : Module R E] →
                [inst_6 : PartialOrder E] →
                  [IsOrderedAddMonoid E] → [PosSMulMono R E] → [OrderClosedTopology E] → ProperCone R E

The positive cone is the proper cone formed by the set of nonnegative elements in an ordered module.

Defined in

Mathlib.Analysis.Convex.Cone.Basic

Cited by

6 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommMonoidTopologicalSpaceModulePartialOrderIsOrderedAddMonoidPosSMulMonoOrderClosedTopology