Reduction by Stages with Topological Conditions

In this chapter we will use the distribution theoretical approach to formulate a reduction by stages theorem that only requires an easily verifiable point set topological condition. This condition is satisfied by a large class of Lie groups, for example, compact ones. Notice that this statement could not have been made had we followed exclusively the purely algebraic approach in §5.2. Having said that, we will analyze the relation between the stages theorem in this chapter and that in the previous one.