Stratified Subcartesian Spaces

Abstract

Abstract We show that if the family of orbits of all vector fields on a subcartesian space P is locally finite and each orbit in is locally closed, then 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 .