[[Geometry MOC]]
# Convex set

Let $S$ be an [[affine space]] (or [[vector space]]) over $\mathbb{R}$[^complex].
A subset $K \sube S$ is said to be **convex** iff for any $x,y \in S$ 
the [[affine combination]] $tx + (1-t)y$ belongs to $K$ for all $t \in [0,1]$. #m/def/geo/affine

  [^complex]: We consider complex vector spaces as real vector spaces of twice the dimension.

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#state/tidy | #lang/en | #SemBr