1. CMB 2011 (vol 54 pp. 693)
 Lusala, Tsasa; Śniatycki, Jędrzej

Stratified Subcartesian Spaces
We show that if the family $\mathcal{O}$ of orbits of all vector fields on
a subcartesian space $P$ is locally finite and each orbit in $\mathcal{O}$
is locally closed, then $\mathcal{O}$ 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 $M/G$.
Keywords:Subcartesian spaces, orbits of vector fields, stratifications, Whitney Conditions Categories:58A40, 57N80 

2. CMB 2009 (vol 53 pp. 340)
3. CMB 2007 (vol 50 pp. 447)
 Śniatycki, Jędrzej

Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces
Let $\mathcal{F}$ be a family of vector fields on a manifold or a
subcartesian space spanning a distribution $D$. We prove that an orbit $O$
of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$
and it has constant rank on $O$. This result implies Frobenius' theorem, and
its various generalizations, on manifolds as well as on subcartesian spaces.
Keywords:differential spaces, generalized distributions, orbits, Frobenius' theorem, Sussmann's theorem Categories:58A30, 58A40 
