We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is continuously reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differenial forms, which statisfies Smith's version of de Rham's theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.

中文翻译：

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次笛卡尔可微空间

我们证明了李群在光滑流形上的适当作用的轨道空间的微分结构是连续自反的。这意味着轨道空间是Smith 意义上的可微空间，保证了轨道空间具有微分形式的外代数，这满足了Smith 版本的de Rham 定理。因为轨道空间是一个局部封闭的次笛卡尔空间，所以它有向量场和它们的流动。