Definition:Convex Set (Vector Space)/Line Segment

Definition
Let $V$ be a vector space over $\R$ or $\C$.

Let $x, y \in V$.

The set:


 * $\left\{{ t x + \left({1 - t}\right) y: t \in \left[{0 \,.\,.\, 1}\right] }\right\}$

is called the (straight) line segment joining $x$ and $y$.

A convex set can thus be described as a set containing all straight line segments between its elements.