Immersion

Are V and W two varieties of class $\{\backslash \; mathcal\; C\}\; ^k$ (possibly K infinite), and F an application of V in W .

It is said that F is a $\{\backslash \; mathcal\; C\}\; ^k$- immersion if pout all X pertaining to V , the row of the tangent linear application Tf (X) is equal to the dimension of W (it is thus surjective).

One differentiates it from:

• the immersion (the row of Tf (X) is the dimension of V )
• of the Plongement (in addition to being an immersion, F is a Homéomorphisme of V on F (V)

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