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Some Results and Problems Concerning Chordal Principal Cluster Sets*

Published online by Cambridge University Press:  22 January 2016

F. Bagemihl
F. Bagemihl*
Affiliation:
University of Wisconsin-Milwaukee
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Let Γ be the unit circle and D be the open unit disk in the complex plane, and denote the Riemann sphere by Ω. By an arc at a point ζ∈Γ we mean a continuous curve such that |z(t)| < 1 for 0 ≦ t < 1 and . A terminal subarc of an arc Λ at ζ is a subarc of the form z = z (t) (t0 ≦ t < 1), where 0 ≦ t0<1. Suppose that f(z) is a meromorphic function in D. Then A(f) denotes the set of asymptotic values of f; and if ζ∈Γ, then C(f, ζ) means the cluster set of f at ζ and is the outer angular cluster set of f at ζ (see [13]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 7 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

Footnotes

*

Research supported by the National Science Foundation.

References

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