We show that a recent cluster set theorem of Rung is sharp in a certain sense. This is accomplished through the construction of an interpolating sequence whose limit set is closed, totally disconnected and porous. The results also generalize some of Dolzenko's cluster set theorems.
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D. Rung and Samih Obaid. "The sharpness of some cluster set results" International Journal of Mathematics and Mathematical Sciences (1987): 777-786. doi:10.1155/S0161171287000863