International Journal of Mathematics and Mathematical Sciences 
Volume 10 (1987), Issue 4, Pages 777-786
doi:10.1155/S0161171287000863

The sharpeness of some cluster set results

D. C. Rung1 and S. A. Obaid2

 1Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA
2Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, San Jose, USA
Received 8 July 1986; Revised 6 October 1986

Abstract

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.