You should give the definitions and state the pertinent results that are needed in your discussion, so your report would be intelligible to other people in the class. No extension on the May 12 deadline will be granted. Here are some suggestions. A. Discuss an equivalent of the Axiom of Choice in an area of mathematics that interests you. In some cases, the original reference given in Rubin and Rubin may be more interesting than their account.
Every group contains a maximal abelian subgroup.
Every free abelian group is projective. The product of compact spaces is compact in the product topology. Every vector space has a basis. A paradoxical decomposition of the sphere. A non-Lebesgue measurable set of real numbers.