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extreme point
Definition 1 Let $C$ be a convex subset of a vector space $X$ . A point $x \in C$ is called an extreme point if it is not an interior point of any line segment in $C$ . That is $x$ is extreme if and only if whenever $x = ty +(1-t)z$ , $t \in (0,1)$ , $z \not= y$ , implies either $y \notin C$ or $z \notin C$ .
For example the set $[0,1] \in {\mathbb{R}}$ is a convex set and $0$ and $1$ are the extreme points.
Bibliography
- 1
- H. L. Royden. Real Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1988
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