Definition:Extreme Point of Convex Set/Definition 1
Jump to navigation
Jump to search
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