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 | References | Similar Articles | Additional Information
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.
- J. E. McMillan, Curvilinear oscillations of holomorphic functions, Duke Math. J. 33 (1966), 495–498. MR 201645
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Keywords:
Principal cluster set,
arc-cluster set diameter,
ambiguous point
Article copyright:
© Copyright 1970
American Mathematical Society