Stratified Subcartesian Spaces

We show that, if the family \cal{O} of orbits of all vector fields on a subcartesian space P is locally finite and each orbit in \cal{O} is locally closed, then \cal{O} defines a smooth Whitney A stratification of P. We also show that the stratification by orbit type of the space M/G of orbits 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.