A necessary condition for principal cluster sets to be void
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 34 #1527.
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