The Packing Constant in l^2, l^p, a Class of Orlicz Functions and its Relationship to Totally Bounded

Link to Master’s project

Abstract. In this paper we will be discussing in further detail papers about the packing constant of the unit sphere in the space l^2, l^p written by Rankin, and a class of Orlicz functions given by Cleaver. In both the l^2 and l^p cases, the packing constant has been found however we will see in a paper written by Cleaver, the packing constant is not easily found for Orlicz spaces. In each case we will relate the packing constant to coverings, and thus relating packing spheres to compactness in metric spaces.