I need your help in defining a boundary for a given convex body, $P$ without knowing the shape of $P$ meaning that I can't say that $P$ is a polygon or any shape which is convex.
Meaning that by using the properties of a convex body I need to define a function or a subset of points which are on the boundary of $P$.
Please help and thanks in advance.
Let $X$ be any topological space, and $A$ be a subset of $X$. A point $p \in A$ is a boundary point if every neighborhood of $p$ contains points on the interior of $A$ and points in the complement of $A$.
This notion is more general, as it does not require $A$ to be convex, or to even be a space with a notion of convexity involved. Since your set has a shape, it probably lives in some nice metric space like $\mathbb R^2$ or something, and so this notion should be really intuitive and geometric.