In sub-Riemannian geometry, the Chow–Rashevskii theorem (also known as Chow's theorem) asserts that any two points of a connected sub-Riemannian manifold, endowed with a bracket generating distribution, are connected by a horizontal path in the manifold.
It is named after Wei-Liang Chow who proved it in 1939, and Petr Konstanovich Rashevskii, who proved it independently in 1938.
The theorem has a number of equivalent statements, one of which is that the topology induced by the Carnot–Carathéodory metric is equivalent to the intrinsic (locally Euclidean) topology of the manifold.
See, for instance, Montgomery (2006) and Gromov (1996).
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