We present some results on the asymptotic paths and asymptotic values for meromorphic functions in an n-fold extended punctured plane \(\widehat{\mathbb{C}}\) \{p1, . . . ,pn}. These results extend some classical results obtained for analytic and meromorphic functions in the complex plane ℂ. In particular, in this more general setting, we present a version of F. Iversen’s result on the existence of asymptotic values of the entire functions in the plane. We also establish a bound for the number of isolated directly critical singularities of a meromorphic function of finite order k with finitely many poles.
