Immersion

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is equivalent to saying that every point in the domain has a neighborhood such that, up to diffeomorphisms of the tangent space, the map looks like the inclusion map from a lower-dimensional Euclidean space to a higher-dimensional Euclidean space.

REFERENCES:

Boy, W. "Über die Curvatura integra und die Topologie geschlossener Flächen." Math. Ann 57, 151-184, 1903.

Pinkall, U. "Models of the Real Projective Plane." Ch. 6 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 63-67, 1986.