International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 777-786
The sharpeness of some cluster set results
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.