Theorems · Definition · convex and discrete geometry

ProperCone.map

{R : Type u_2} →
  {E : Type u_3} →
    {F : Type u_4} →
      [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 : AddCommMonoid F] →
                    [inst_7 : TopologicalSpace F] →
                      [inst_8 : Module R F] →
                        [ContinuousAdd F] → [ContinuousConstSMul R F] → (E →L[R] F) → ProperCone R E → ProperCone R F

The closure of image of a proper cone under a linear map is a proper cone. We use continuous maps here to match ProperCone.comap.

Defined in

Mathlib.Analysis.Convex.Cone.Basic

Cited by

6 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommMonoidTopologicalSpaceModuleAddCommMonoidTopologicalSpaceModuleContinuousAddContinuousConstSMul