properties of extreme subsets of a closed convex setPropertiesOfExtemeSubsetsOfAClosedConvexSet2005-07-24 05:39:072005-07-25 17:07:48Theorem% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $K$ be a closed \PMlinkname{convex subset}{ConvexSet} of a normed vector space
\begin{enumerate}
\item 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 $K$
\item $A\subset B\subset K$ such as $A,B$ are extreme subsets of $B$ and $K$ respectively. Then $A$ is an extreme subset of $K$.
\end{enumerate}