  We introduce the self-linking number of a smooth closed curve in R^n with
respect to a 3-dimensional vector bundle over the curve, provided that some
regularity conditions are satisfied. When n=3, this construction gives the
classical self-linking number of a closed embedded curve with non-vanishing
curvature. We also look at some interesting particular cases, which correspond
to the osculating or the orthogonal vector bundle of the curve.
