International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 777-786

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

Copyright © 1987 D. C. Rung and S. A. Obaid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.