Convex set

Let $𝑆$ be an affine space (or vector space) over $ℝ$ ¹. A subset $𝐾 \subseteq 𝑆$ is said to be convex iff for any $𝑥, 𝑦 \in 𝑆$ the affine combination $𝑡 𝑥 + (1 - 𝑡) 𝑦$ belongs to $𝐾$ for all $𝑡 \in [0, 1]$ . affine