# Definition The cotangent space $T^*_P$ at point $P\in M$ where $M$ is a [[manifold]] is the dual space to the [[tangent space]] $T_P$ at $P$. It is the space of [[One-Form]] at $P$. The two spaces are said to be dual to one another since one can also think of vectors as linear functions that map a one-form to a real number, $\tilde{\omega}(\pmb{V}) \equiv \pmb{V}(\tilde{\omega})$