The mathematical technique called "general position" implies that for a given "n"-sphere in "m"-dimensional Euclidean space, if "m" is large enough (depending on "n"), the sphere should be unknotted. In general, piecewise-linear "n"-spheres form knots only in ("n" + 2)-dimensional space , although this is no longer a requirement for smoothly knotted spheres. In fact, there are smoothly knotted formula_34-spheres in 6"k"-dimensional space; e.g., there is a smoothly knotted 3-sphere in formula_35 . Thus the codimension of a smooth knot can be arbitrarily large when not fixing the dimension of the knotted sphere; however, any smooth "k"-sphere embedded in formula_36 with formula_37 is unknotted. The notion of a knot has further generalisations in mathematics, see: Knot (mathematics), isotopy classification of embeddings.