extreme point

Definition.

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 $x=ty+(1-t)z$, $t\in (0,1)$, $z\ne y$, implies either $y\notin C$ or $z\notin C$.

For example the set $[0,1]\in ℝ$ is a convex set and $0$ and $1$ are the extreme points.

Title	extreme point
Canonical name	ExtremePoint
Date of creation	2013-03-22 14:24:55
Last modified on	2013-03-22 14:24:55
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	7
Author	jirka (4157)
Entry type	Definition
Classification	msc 52A99
Related topic	FaceOfAConvexSet
Related topic	ExposedPointsAreDenseInTheExtremePoints