Geodesic
Stratified Subcartesian Spaces
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 693-705

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DOI

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 $M/G$ .
DOI : 10.4153/CMB-2011-026-3
Mots-clés : 58A40, 57N80, Subcartesian spaces, orbits of vector fields, stratifications, Whitney Conditions 
Lusala, Tsasa; Śniatycki, Jędrzej. Stratified Subcartesian Spaces. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 693-705. doi: 10.4153/CMB-2011-026-3
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     title = {Stratified {Subcartesian} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {693--705},
     year = {2011},
     volume = {54},
     number = {4},
     doi = {10.4153/CMB-2011-026-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-026-3/}
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