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In mathematics, more specifically differential topology, a local diffeomorphism is intuitively a function between smooth manifolds that preserves the local differentiable structure. The formal definition of a local diffeomorphism is given below. ==Formal definition== Let ''X'' and ''Y'' be differentiable manifolds. A function, : is a local diffeomorphism, if for each point ''x'' in ''X'', there exists an open set ''U'' containing ''x'', such that : is open in ''Y'' and : is a diffeomorphism. A local diffeomorphism is a special case of an immersion ''f'' from ''X'' to ''Y'', where the image ''f''(''U'') of ''U'' under ''f'' locally has the differentiable structure of a submanifold of ''Y''. Then ''f''(''U'') and ''X'' may have a lower dimension than ''Y''. 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「local diffeomorphism」の詳細全文を読む スポンサード リンク
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