Theorems · Definition · convex and discrete geometry

Convexity.ConvexSpace.mk

{R : Type u_1} →
  [inst : PartialOrder R] →
    [inst_1 : Semiring R] →
      [inst_2 : IsStrictOrderedRing R] →
        {M : Type u_9} →
          (sConvexComb : Convexity.StdSimplex R M → M) →
            (∀ (x : M), sConvexComb (Convexity.StdSimplex.single x) = x) →
              (∀ (f : Convexity.StdSimplex R (Convexity.StdSimplex R M)),
                  sConvexComb (Convexity.StdSimplex.map sConvexComb f) = sConvexComb (Convexity.sConvexComb f)) →
                Convexity.ConvexSpace R M

The public constructor for ConvexSpace.

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRing