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. The axiom of multiple choice. E. A significant theorem in any area of mathematics that employs the Axiom of Choice in its proof.