Let $X$ be a compact Riemann surface, and denote by $m_X$ the following field: $ m_X := \{ f:X \to \mathbb{P}_\mathbb{C} : f- \text{meromorphic} \} - \{\infty \} $
What is the natural injection of the field of rational functions $\mathbb{C}(z)$ into $m_X$ ?
p.s- $\mathbb{P}_\mathbb{C}$ denotes the Riemann sphere.
Thanks in advance !!!