\begin{definition}[Definition:Extreme Point of Convex Set]
Let $X$ be a vector space over $\R$. 
Let $K$ be a convex subset of $X$. 
We say that $a$ is an '''extreme point''' of $K$ {{iff}}:
:whenever $a = t x + \paren {1 - t} y$ for $t \in \openint 0 1$, we have $x = y = a$.
\end{definition}