A necessary condition for principal cluster sets to be void
Abstract: Let be an arbitrary function from the open unit disk into the Riemann sphere , and let be a point on the unit circle . We prove that if the principal cluster set of at is void, then either is an ambiguous point of or the diameter of each arc-cluster set of at is greater than a fixed positive number.
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Keywords: Principal cluster set, arc-cluster set diameter, ambiguous point
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