properties of extreme subsets of a closed convex set
Let $K$ be a closed convex subset (http://planetmath.org/ConvexSet) of a normed vector space^{}

1.
If $\{{A}_{i}:i\in I\}$ is a family of extreme subsets of $K$, such as ${\bigcap}_{i\in I}{A}_{i}\ne \mathrm{\varnothing}$ then ${\bigcap}_{i\in I}{A}_{i}$ is extreme subset of $K$

2.
$A\subset B\subset K$ such as $A,B$ are extreme subsets of $B$ and $K$ respectively. Then $A$ is an extreme subset of $K$.
Title  properties of extreme subsets of a closed convex set 

Canonical name  PropertiesOfExtremeSubsetsOfAClosedConvexSet 
Date of creation  20130322 15:24:46 
Last modified on  20130322 15:24:46 
Owner  georgiosl (7242) 
Last modified by  georgiosl (7242) 
Numerical id  7 
Author  georgiosl (7242) 
Entry type  Theorem 
Classification  msc 52A99 
Related topic  ConvexSet 