Plunging

In the differential Topology, is V and W two varieties of class {\ mathcal C} ^k (possibly K infinite), and F an application of V in W .

It is said that F is a {\ mathcal C} ^k- plunging so for all X pertaining to V , the row of the tangent linear application Tf (X) is equal to the dimension of V (it is thus injective), and if moreover F is a Homéomorphisme of V on F (V) .

One differentiates it from

  • the immersion (the row of Tf (X) is the dimension of V )
  • the Submersion (the row of Tf (X) is the dimension of W )

Abstractedly

A plunging is defined in the selected ambient category. In C of Category, for two objects X, Y over there, we said that X is plunged in Y if exists C morphism (plunging) between them which is injective

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