A space of meromorphic functions

Mittag–Leffler's classical theorem on the expansion of a meromorphic function into partial fractions leads naturally to the construction of a topological nonvector space $\mathfrak M_{M\Pi}$. Several properties of this space are studied, the notion of a Mittag–Leffler basis is introduced, and a generalization of Mittag–Leffler's theorem is proved.