Editing Extreme point (section)

==Examples==

If <math>a < b</math> are two real numbers then <math>a</math> and <math>b</math> are extreme points of the interval <math>[a, b].</math> However, the open interval <math>(a, b)</math> has no extreme points.{{sfn |Narici|Beckenstein|2011|pp=275-339}} 
Any [[open interval]] in <math>\R</math> has no extreme points while any non-degenerate [[closed interval]] not equal to <math>\R</math> does have extreme points (that is, the closed interval's endpoint(s)).  More generally, any [[Open set|open subset]] of finite-dimensional [[Euclidean space]] <math>\R^n</math> has no extreme points.

The extreme points of the [[closed unit disk]] in <math>\R^2</math> is the [[unit circle]]. 

The perimeter of any convex polygon in the plane is a face of that polygon.{{sfn|Narici|Beckenstein|2011|pp=275-339}} 
The vertices of any convex polygon in the plane <math>\R^2</math> are the extreme points of that polygon. 

An injective linear map <math>F : X \to Y</math> sends the extreme points of a convex set <math>C \subseteq X</math> to the extreme points of the convex set <math>F(X).</math>{{sfn|Narici|Beckenstein|2011|pp=275-339}} This is also true for injective affine maps.