> 
> Let $A$ be a **compact convex set** in $\mathbb{R}^2$.
> 
> 
> 

What does ''compact convex set'' mean?

What I understand: We have a "bunch" of real points $(x,y)$ in the plane. Any two of them satisfies the fact that a line drawn between them is fully inside this "bunch" of points.

So can this "bunch" be a polygon? (I think it can.)   

Also, how does the **compact** part fit in and what does it mean?   

How do I make one in the plane?   

Also what is a "compact convex polygon" if it is possible?