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# Stratified Subcartesian Spaces

Published:2011-03-05
Printed: Dec 2011
• Tsasa Lusala,
Department of Mathematics and Statistics, University of Calgary, Calgary, AB
• Jędrzej Śniatycki,
Department of Mathematics and Statistics, University of Calgary, Calgary, AB
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## Abstract

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
 MSC Classifications: 58A40 - Differential spaces 57N80 - Stratifications

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