Definition:Extreme Point of Convex Set/Definition 1

Definition
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 $K$ :


 * whenever $a = t x + \paren {1 - t} y$ for $t \in \openint 0 1$, we have $x = y = a$.