# 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. 1.

If $\{A_{i}\colon i\in I\}$ is a family of extreme subsets of $K$, such as $\bigcap_{i\in I}A_{i}\neq\emptyset$ then $\bigcap_{i\in I}A_{i}$ is extreme subset of $K$

2. 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 PropertiesOfExtremeSubsetsOfAClosedConvexSet 2013-03-22 15:24:46 2013-03-22 15:24:46 georgiosl (7242) georgiosl (7242) 7 georgiosl (7242) Theorem msc 52A99 ConvexSet