The Hahn-banach Separation Theorem and Other Separation Results

This paper will introduce and prove several theorems involving the separation of convex sets by hyperplanes, along with other interesting related results. It will begin with some basic separation results in Rn, such as the Hyperplane Separation Theorem of Hermann Minkowski, and then it will focus on and prove the extension of this theorem into normed vector spaces, known as the Hahn-Banach Separation Theorem. This paper will also prove some supporting results as stepping stones along the way, such as the Supporting Hyperplane Theorem and the analytic Hahn-Banach Theorem.