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Proceedings of the American Mathematical Society

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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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DOI: https://doi.org/10.1090/S0002-9939-1970-0247096-9
Keywords: Principal cluster set, arc-cluster set diameter, ambiguous point
Article copyright: © Copyright 1970 American Mathematical Society

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