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