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 $K$ if and only if:

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

Sources

• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $21.6$: The Krein-Milman Theorem