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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 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. A stronger statement that implies the theorem is the ball–box theorem. See, for instance, and . ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chow–Rashevskii theorem」の詳細全文を読む スポンサード リンク
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