In the mathematical field of functional analysis, the space denoted by c is the vector space of all convergent sequences of real numbers or complex numbers. When equipped with the uniform norm: the space c becomes a Banach space. It is a closed linear subspace of the space of bounded sequences, \ell^\infty, and contains as a closed subspace the Banach space c_0 of sequences converging to zero. The dual of c is isometrically isomorphic to \ell^1, as is that of c_0. In particular, neither c nor c_0 is reflexive. In the first case, the isomorphism of \ell^1 with c^* is given as follows. If then the pairing with an element in c is given by This is the Riesz representation theorem on the ordinal \omega. For c_0, the pairing between in \ell^1 and in c_0 is given by