Stratified Subcartesian Spaces

摘要

We show that if the family O of orbits of all vector fields on a subcartesian space P is locally finite and each orbit in O is locally closed, then O defines a smooth Whitney A stratification of P. We also show that the stratification by orbit type of the space of orbits M/G of a proper action of a Lie group G on a smooth manifold M is given by orbits of the family of all vector fields on M/G.