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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A necessary condition for principal cluster sets to be void


Author: C. L. Belna
Journal: Proc. Amer. Math. Soc. 24 (1970), 90-91
MSC: Primary 30.62
DOI: https://doi.org/10.1090/S0002-9939-1970-0247096-9
MathSciNet review: 0247096
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Abstract: Let $f$ be an arbitrary function from the open unit disk $D$ into the Riemann sphere $W$, and let $p$ be a point on the unit circle $C$. We prove that if the principal cluster set of $f$ at $p$ is void, then either $p$ is an ambiguous point of $f$ or the diameter of each arc-cluster set of $f$ at $p$ is greater than a fixed positive number.


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Keywords: Principal cluster set, arc-cluster set diameter, ambiguous point
Article copyright: © Copyright 1970 American Mathematical Society