Advanced Geometry - Convex sets and Extreme points proof

Let K subset of R^n be a convex set. We call x1 element of K an extreme point of K if K/{x1} is convex too.

Prove that x1 element of K is an extreme point iff cx + (1-c)y = x1 for 0<c<1, c element of R (real numbers as above) implies x = y = x1.

any answer or help will be greatly appreciated.

Re: Advanced Geometry - Convex sets and Extreme points proof

I know it's hard but anything written down could be good.

Re: Advanced Geometry - Convex sets and Extreme points proof

Re: Advanced Geometry - Convex sets and Extreme points proof

thank you very much. i understand now. btw where do you get all those symbols and mathematical notation to make posts with?

Re: Advanced Geometry - Convex sets and Extreme points proof

Quote:

Originally Posted by

**maxgunn555** where do you get all those symbols and mathematical notation to make posts with?

Look at the "sticky" posts in the LaTeX help forum.