N m is called an immersion if the rank of f is 11, the dimension of the domain M, at all points of M. : 11, and it is clear from Theorem 10(2) that an immersion is locally one-one (so it is a topological immersion, as defined in Chapter I). On the other hand, a differentiable map f need not be an immersion even if it is globally one-one.

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A Comprehensive Introduction To Differential Geometry by Michael Spivak

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