Corollary: Intersection of Convex Affine Sets

(related to Definition: Convex Affine Set)

Let \(\mathcal C\) be a family of convex subsets \(C\) of an \(n\)-dimensional affine space \(\mathcal A=(A,V_A,v)\) with \(V_A\) as the associated vector space over the field \(\mathbb R\) of real numbers. It follows immediately from the definition of convex affine sets that any intersection of convex sets \(\bigcap \mathcal C\) is again convex.

Proofs: 1

Definitions: 1

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  1. Ziegler, G√ľnter M.: "Lectures on Polytopes", Springer Verlag, 1994