An Attainable Separation Theorem For A Finite Number Of Non Intersect Closed Sets

The separation theorems play an important role in functional analysis and op-timization theory. Using the technique of variational analysis and in terms of normal cones, we establish the attainable separation theorem for finitely many closed set-s,which covers a well-known classical convex separation theorem.At the end of this paper,we give a comparison between the nonconvex separation theorem and the extremal principle.