Complex sentence: In other words, one can choose any complex numbers from the bounded connected components of C\\ "K" and the theorem guarantees the existence of a sequence of rational functions with poles only amongst those chosen numbers.
Split into simpler sentences: In other words, one can pick any complex numbers as one wishes from the bounded connected components of C\\ "K". Then the theorem guarantees the existence of a sequence of rational functions with poles only in those chosen numbers.