I want to construct an example that a point is extreme but is not exposed. This example can be in the following :
A compact convex subset $K\subset\mathbb{R}^{2}$ and a point $u\in K$ such that $u$ is an extreme point of $K$, but is not an exposed point of $K$.
Also,
Every denting point is extreme and strongly exposed point.
I want to understand these proofs.
