Theorems · Inductive type · convex and discrete geometry

Convexity.IsAffineMap

(R : Type u_1) →
  {M : Type u_3} →
    {N : Type u_4} →
      [inst : PartialOrder R] →
        [inst_1 : Semiring R] →
          [inst_2 : IsStrictOrderedRing R] → [Convexity.ConvexSpace R M] → [Convexity.ConvexSpace R N] → (M → N) → Prop

A map between convex spaces is affine if it preserves convex combinations. TODO: Show that this generalises affine maps between affine spaces, see AffineMap.

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

33 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace