Kybernetika

Given a closed convex subset $A$ of a Hausdorff locally convex space $X$ and a point $x \notin A$, does there exist a nonzero continuous linear functional $\varphi \in X^*$ such that $\varphi (x) = \sup \varphi (A)$? In this work the just defined problem is dealt with and obtained results are then applied to establish some strong duality principles concerning the surrogate reverse duality.