Convex geometry/Convex subsets/Convex (R n)/Definition

Convex subset

A subset ${}T\subseteq \mathbb {R} ^{n}$ is called convex if for any two points ${}P,Q\in T$, the line segment between the two points, that is, every point of the form

$rP+(1-r)Q{\text{ with }}r\in [0,1],$

also belongs to ${}T$.