My question is about the support function defined $$s_{A}(x)= \sup \{x\cdot a | a \in A\}$$ ($A\subset R^{n}, x \in S^{n}$).(more generally it can be taken to be other scalar product.) So the function is defined on sets, and generally for the convex sets (as supporting hyperplanes are well used for exactly convex bodies). I just wanted to know if the following can be true or not. $$s_{A}(x) = s_{\partial A}(x)$$
I'm sorry if the quesion is inappropriate. Thank you.