\begin{definition}[Definition:Convex Set (Vector Space)]
Let $V$ be a vector space over $\R$ or $\C$.
A subset $A \subseteq V$ is said to be '''convex''' {{iff}}:
:$\forall x, y \in A: \forall t \in \closedint 0 1: t x + \paren {1 - t} y \in A$
\end{definition}