Given an "n"-dimensional smooth manifold "M", and a point , a contact element of "M" with contact point "p" is an ("n" − 1)-dimensional linear subspace of the tangent space to "M" at "p". A contact element can be given by the kernel of a linear function on the tangent space to "M" at "p". However, if a subspace is given by the kernel of a linear function ω, then it will also be given by the zeros of λω where is any nonzero real number. Thus, the kernels of all give the same contact element. It follows that the space of all contact elements of "M" can be identified with a quotient of the cotangent bundle T*"M" (with the zero section formula_1 removed), namely: