Let $K$ be a closed convex subset of a normed vector space

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. $A\subset B\subset K$ such as $A,B$ are extreme subsets of $B$ and $K$ respectively. Then $A$ is an extreme subset of $K$