The separation theorems are the key results for convex programming. They are important consequences of the Hahn-Theorem theorem. In this work begin to consider vector spaces, in general, then normed spaces and lastly Hilbert spaces. In the end, applications of these results in convex programming and in minimax theorem, two important tools in operations research, management and economics are presented.

--

Hahn-Banach theorem,Separation theorems,Convex programming,Minimax theorem